Geometry & Trigonometry Problems MCQs

Solved Geometry & Trigonometry Problems MCQs with answers and explanations. Free practice questions for PPSC, FPSC, CSS and other government job exams on FreeSekho.

1. 1. The tangent to a circle is always what to the radius at the point of contact?

   1. Perpendicular ✓
   2. Parallel
   3. At 60°
   4. At 45°

2. 2. A right triangle has a hypotenuse of 25 and one leg of 7. What is the length of the other leg?

   1. 23
   2. 20
   3. 18
   4. 24 ✓

3. 3. Solve for θ (0° ≤ θ ≤ 90°): tan θ = 1

   1. 90°
   2. 60°
   3. 30°
   4. 45° ✓

4. 4. What is the sum of the interior angles of a pentagon?

   1. 360°
   2. 450°
   3. 720°
   4. 540° ✓

5. 5. If sin θ = 3/5 and θ is acute, what is cos θ?

   1. 4/5 ✓
   2. 5/4
   3. 3/4
   4. 5/3

6. 6. In a right triangle, cosine of an angle is defined as which ratio?

   1. Opposite side / Adjacent side
   2. Opposite side / Hypotenuse
   3. Hypotenuse / Adjacent side
   4. Adjacent side / Hypotenuse ✓

7. 7. A triangle containing a 90° angle is called what?

   1. Right triangle ✓
   2. Obtuse triangle
   3. Acute triangle
   4. Equilateral triangle

8. 8. What is the volume of a sphere with radius 3? (Use pi ≈ 3.14; formula (4/3)πr³)

   1. 84.78
   2. 28.26
   3. 37.68
   4. 113.04 ✓

9. 9. In a right triangle, the hypotenuse is 8 and one angle is 45°. What is the length of each leg?

   1. 5.66 ✓
   2. 8
   3. 6.93
   4. 4

10. 10. A kite is flying at the end of a 100 m string, making an angle of 30° with the ground. What is the height of the kite?

    1. 100 m
    2. 70.7 m
    3. 50 m ✓
    4. 86.6 m

11. 11. What is the distance between points (-1, -1) and (2, 3)?

    1. 3
    2. 7
    3. 4
    4. 5 ✓

12. 12. Solve for θ (0° ≤ θ ≤ 90°): sin θ = 1/2

    1. 30° ✓
    2. 45°
    3. 60°
    4. 90°

13. 13. What is the value of 2 sin 45° * cos 45°?

    1. 2
    2. 0.5
    3. 0
    4. 1 ✓

14. 14. If cos θ = 5/13 and θ is acute, what is sin θ?

    1. 13/12
    2. 5/12
    3. 12/13 ✓
    4. 12/5

15. 15. A right triangle has legs of 7 and 24. What is the length of the hypotenuse?

    1. 28
    2. 26
    3. 25 ✓
    4. 23

16. 16. Solve for θ (0° ≤ θ ≤ 90°): sin θ = 1

    1. 0°
    2. 90° ✓
    3. 45°
    4. 60°

17. 17. A right triangle has legs of 6 and 8. What is the length of the hypotenuse?

    1. 10 ✓
    2. 9
    3. 12
    4. 14

18. 18. A quadrilateral with opposite sides parallel and equal, but angles not necessarily 90°, is called what?

    1. Rectangle
    2. Square
    3. Parallelogram ✓
    4. Trapezoid

19. 19. If tan θ = 3/4 and θ is acute, what is sin θ?

    1. 4/3
    2. 3/4
    3. 4/5
    4. 3/5 ✓

20. 20. Solve for θ (0° ≤ θ ≤ 90°): cos θ = 0

    1. 45°
    2. 30°
    3. 90° ✓
    4. 0°

21. 21. A tree breaks and falls such that the top touches the ground at a distance of 8 m from the base, making an angle of 45° with the ground. What was the length of the broken part?

    1. 8 m
    2. 16 m
    3. 4√2 m
    4. 8√2 (≈11.31 m) ✓

22. 22. What is the value of sin 45°?

    1. 1/sqrt(2) ✓
    2. sqrt(3)/2
    3. 1
    4. 1/2

23. 23. What is the perimeter of an equilateral triangle with side length 9?

    1. 27 ✓
    2. 18
    3. 81
    4. 36

24. 24. The point where the three angle bisectors of a triangle meet is called what?

    1. Centroid
    2. Circumcenter
    3. Incenter ✓
    4. Orthocenter

25. 25. A quadrilateral with all four sides equal and all angles 90° is called what?

    1. Rhombus
    2. Rectangle
    3. Trapezoid
    4. Square ✓

26. 26. The three medians of a triangle intersect at a point called what?

    1. Circumcenter
    2. Orthocenter
    3. Incenter
    4. Centroid ✓

27. 27. Convert 45° to radians.

    1. π/3
    2. π/4 ✓
    3. π/6
    4. π/2

28. 28. The area of a triangle with base 8 and height 5 is:

    1. 40
    2. 13
    3. 20 ✓
    4. 26

29. 29. In a right triangle, one leg is 10 and the angle opposite to it is 30°. What is the length of the hypotenuse?

    1. 5
    2. 20 ✓
    3. 10
    4. 17.32

30. 30. What type of angle measures more than 90° but less than 180°?

    1. Obtuse angle ✓
    2. Straight angle
    3. Acute angle
    4. Right angle

31. 31. Convert 90° to radians.

    1. 2π
    2. π/2 ✓
    3. π
    4. π/4

32. 32. Convert π/6 radians to degrees.

    1. 60°
    2. 30° ✓
    3. 45°
    4. 90°

33. 33. What is the value of sin 30° + cos 60°?

    1. 0.5
    2. 1 ✓
    3. 1.5
    4. 0

34. 34. What is the surface area of a cuboid with dimensions 5, 4, and 3?

    1. 60
    2. 47
    3. 94 ✓
    4. 24

35. 35. In a triangle, if two angles measure 90° and 40°, what is the third angle?

    1. 70°
    2. 40°
    3. 50° ✓
    4. 60°

36. 36. What is the value of sin 15° + sin 75°?

    1. 1
    2. 2
    3. √2
    4. √6/2 (≈1.22) ✓

37. 37. What is the volume of a cone with radius 3, height 7? (Use pi = 22/7; formula (1/3)πr²h)

    1. 44
    2. 66 ✓
    3. 22
    4. 198

38. 38. Each interior angle of a regular hexagon measures:

    1. 120° ✓
    2. 135°
    3. 144°
    4. 108°

39. 39. What type of angle measures exactly 90°?

    1. Straight angle
    2. Acute angle
    3. Right angle ✓
    4. Obtuse angle

40. 40. What are angles called that are opposite each other when two lines cross?

    1. Vertically opposite angles ✓
    2. Complementary angles
    3. Supplementary angles
    4. Adjacent angles

41. 41. What type of angle measures more than 180° but less than 360°?

    1. Straight angle
    2. Obtuse angle
    3. Acute angle
    4. Reflex angle ✓

42. 42. What is the volume of a cylinder with radius 7 and height 10? (Use pi = 22/7)

    1. 220
    2. 1540 ✓
    3. 770
    4. 440

43. 43. What is cos(90° - θ) equal to?

    1. -cos θ
    2. cos θ
    3. sin θ ✓
    4. -sin θ

44. 44. Using Heron's formula, find the area of a triangle with sides 7, 8, and 9.

    1. 36
    2. 26.83 (approx) ✓
    3. 24
    4. 31.5

45. 45. What is the value of tan 45°?

    1. 1/sqrt(3)
    2. 0
    3. 1 ✓
    4. sqrt(3)

46. 46. What is the perimeter of a rectangle with length 8 and width 5?

    1. 40
    2. 26 ✓
    3. 45
    4. 13

47. 47. What is the slope of the line through points (0, 0) and (5, 10)?

    1. 1/2
    2. 5
    3. 10
    4. 2 ✓

48. 48. Two angles that add up to 180° are called what?

    1. Vertical angles
    2. Corresponding angles
    3. Supplementary angles ✓
    4. Complementary angles

49. 49. An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. If those two interior angles are 35° and 65°, what is the exterior angle?

    1. 100° ✓
    2. 90°
    3. 80°
    4. 130°

50. 50. What is the sum of the interior angles of a triangle?

    1. 270°
    2. 360°
    3. 90°
    4. 180° ✓

51. 51. In a right triangle, tangent of an angle is defined as which ratio?

    1. Hypotenuse / Adjacent side
    2. Opposite side / Hypotenuse
    3. Adjacent side / Opposite side
    4. Opposite side / Adjacent side ✓

52. 52. The angle of depression from the top of a 30 m cliff to a boat is 30°. How far is the boat from the base of the cliff?

    1. 51.96 m ✓
    2. 30 m
    3. 15 m
    4. 60 m

53. 53. Angles in the same segment of a circle, subtended by the same arc, are always what?

    1. Different
    2. Equal ✓
    3. Supplementary
    4. Complementary

54. 54. What is the total surface area of a cylinder with radius 7 and height 10? (Use pi = 22/7; formula 2πr(h+r))

    1. 308
    2. 748 ✓
    3. 440
    4. 1540

55. 55. A quadrilateral with exactly one pair of parallel sides is called what?

    1. Square
    2. Rhombus
    3. Parallelogram
    4. Trapezoid ✓

56. 56. A right triangle has legs of 8 and 15. What is the length of the hypotenuse?

    1. 21
    2. 19
    3. 16
    4. 17 ✓

57. 57. What is the volume of a cuboid with length 10, width 6, and height 5?

    1. 300 ✓
    2. 150
    3. 21
    4. 60

58. 58. A ladder 10 m long leans against a wall, reaching 6 m up the wall. How far is the foot of the ladder from the wall?

    1. 6 m
    2. 8 m ✓
    3. 4 m
    4. 16 m

59. 59. What is the midpoint of the segment joining (0, 0) and (10, 6)?

    1. (10, 6)
    2. (0, 3)
    3. (5, 6)
    4. (5, 3) ✓

60. 60. What is the reciprocal of sine called?

    1. Cosine
    2. Cosecant ✓
    3. Secant
    4. Cotangent

61. 61. The point equidistant from all three vertices of a triangle is called what?

    1. Incenter
    2. Circumcenter ✓
    3. Centroid
    4. Orthocenter

62. 62. What is the perimeter of a right triangle with legs 3 and 4 (hypotenuse 5)?

    1. 12 ✓
    2. 10
    3. 7
    4. 24

63. 63. A triangle containing one angle greater than 90° is called what?

    1. Obtuse triangle ✓
    2. Right triangle
    3. Acute triangle
    4. Equilateral triangle

64. 64. What is the area of a circle with radius 7? (Use pi = 22/7)

    1. 44
    2. 154 ✓
    3. 308
    4. 49

65. 65. A quadrilateral with all four sides equal but angles not necessarily 90° is called what?

    1. Trapezoid
    2. Rectangle
    3. Rhombus ✓
    4. Square

66. 66. If tan θ = 3/4 and θ is acute, what is cos θ?

    1. 4/5 ✓
    2. 5/4
    3. 3/4
    4. 3/5

67. 67. A right triangle has legs of 1 and 1. What is the length of the hypotenuse?

    1. sqrt(2) ✓
    2. sqrt(3)
    3. 2
    4. 1

68. 68. What is the area of a parallelogram with base 10 and height 4?

    1. 28
    2. 40 ✓
    3. 14
    4. 20

69. 69. If the angle of elevation of the sun is 60° and a tower is 10√3 m tall, what is the length of its shadow?

    1. 20 m
    2. 5 m
    3. 10 m ✓
    4. 17.32 m

70. 70. What is tan(90° - θ) equal to?

    1. -tan θ
    2. cot θ ✓
    3. tan θ
    4. -cot θ

71. 71. If the angle of elevation of the top of a tower from a point 30 m away is 60°, what is the height of the tower (approx)?

    1. 30 m
    2. 60 m
    3. 17.32 m
    4. 51.96 m ✓

72. 72. A ladder 13 m long leans against a wall, with its foot 5 m from the wall base. How high up the wall does the ladder reach?

    1. 18 m
    2. 10 m
    3. 12 m ✓
    4. 8 m

73. 73. In a right triangle with angles 30°-60°-90°, if the hypotenuse is 12, what is the side opposite the 30° angle?

    1. 12
    2. 6 ✓
    3. 4
    4. 6√3

74. 74. What is the perimeter of a square with side length 7?

    1. 14
    2. 28 ✓
    3. 49
    4. 21

75. 75. What is the diameter of a circle with radius 9?

    1. 27
    2. 4.5
    3. 9
    4. 18 ✓

76. 76. If the slope between (2, k) and (5, 7) is 1, what is k?

    1. 4 ✓
    2. 3
    3. 10
    4. 1

77. 77. Equal chords of a circle are equidistant from what?

    1. Each other
    2. The center ✓
    3. The circumference
    4. The diameter only

78. 78. In a right triangle, the hypotenuse is 10 and one angle is 30°. What is the length of the side opposite to 30°?

    1. 8.66
    2. 5 ✓
    3. 10
    4. 2.5

79. 79. Which identity is always true for any angle θ, relating tan and sec?

    1. tan²θ - 1 = sec²θ
    2. 1 + tan²θ = csc²θ
    3. 1 + tan²θ = sec²θ ✓
    4. 1 - tan²θ = sec²θ

80. 80. What is the value of sin 60°?

    1. 1/2
    2. sqrt(3)/2 ✓
    3. 1/sqrt(2)
    4. 1

81. 81. The point where the three altitudes of a triangle meet is called what?

    1. Orthocenter ✓
    2. Circumcenter
    3. Centroid
    4. Incenter

82. 82. What is the area of an equilateral triangle with side length 4?

    1. 4
    2. 4√3 (≈6.93) ✓
    3. 16
    4. 8

83. 83. What is the reciprocal of cosine called?

    1. Cosecant
    2. Cotangent
    3. Sine
    4. Secant ✓

84. 84. What is sin(90° - θ) equal to?

    1. -cos θ
    2. cos θ ✓
    3. sin θ
    4. -sin θ

85. 85. What is the slope of the line through points (3, 4) and (7, 4)?

    1. 1
    2. Undefined
    3. 0 ✓
    4. 4

86. 86. What is the value of cos²60° + sin²60°?

    1. 2
    2. 1 ✓
    3. 0.5
    4. 0

87. 87. What is the sum of the interior angles of a hexagon?

    1. 540°
    2. 720° ✓
    3. 360°
    4. 900°

88. 88. What is the term for a region bounded by a chord and the arc it cuts off?

    1. Radius
    2. Diameter
    3. Segment ✓
    4. Sector

89. 89. What type of angle measures exactly 180°?

    1. Reflex angle
    2. Right angle
    3. Obtuse angle
    4. Straight angle ✓

90. 90. What is the area of a circle with diameter 10? (Use pi = 3.14)

    1. 31.4
    2. 25
    3. 78.5 ✓
    4. 157

91. 91. In a right triangle with angles 30°-60°-90°, if the shortest side (opposite 30°) is 5, what is the side opposite 60°?

    1. 5√3 (≈8.66) ✓
    2. 10
    3. 5
    4. 5√2

92. 92. What is the value of sin²30° + cos²30°?

    1. 0.5
    2. 1 ✓
    3. 0
    4. 2

93. 93. What is the area of a square with side length 7?

    1. 14
    2. 21
    3. 49 ✓
    4. 28

94. 94. A right triangle has one angle of 30° and the side opposite to it is 7. What is the hypotenuse?

    1. 14 ✓
    2. 3.5
    3. 7
    4. 12.12

95. 95. The angle subtended by an arc at the center is how many times the angle subtended at the remaining circumference?

    1. Twice ✓
    2. Equal
    3. Half
    4. Three times

96. 96. The area of a triangle with base 10 and height 6 is:

    1. 16
    2. 20
    3. 30 ✓
    4. 60

97. 97. What is the value of sin 30°?

    1. 1
    2. sqrt(3)/2
    3. 1/2 ✓
    4. 0

98. 98. If the angle of elevation of the sun is 45° and a pole casts a shadow of 6 m, what is the height of the pole?

    1. 8.49 m
    2. 3 m
    3. 12 m
    4. 6 m ✓

99. 99. From a point on the ground 50 m from the base of a tower, the angle of elevation of the top is 45°. What is the height of the tower?

    1. 100 m
    2. 50 m ✓
    3. 70.71 m
    4. 25 m

100. 100. Using Heron's formula, find the area of a triangle with sides 3, 4, and 5.

     1. 6 ✓
     2. 10
     3. 12
     4. 7.5

101. 101. If sin θ = 0.6, what is sin²θ + cos²θ?

     1. 0.64
     2. 0.36
     3. 1.36
     4. 1 ✓

102. 102. Solve for θ (0° ≤ θ ≤ 90°): cos θ = 1/2

     1. 30°
     2. 60° ✓
     3. 45°
     4. 90°

103. 103. What is the slope of a line perpendicular to a line with slope 2?

     1. 2
     2. -2
     3. 1/2
     4. -1/2 ✓

104. 104. A triangle in which all angles are less than 90° is called what?

     1. Acute triangle ✓
     2. Isosceles triangle
     3. Right triangle
     4. Obtuse triangle

105. 105. The perpendicular from the center of a circle to a chord does what to the chord?

     1. Bisects it ✓
     2. Halves the angle only
     3. Has no special relationship to it
     4. Doubles it

106. 106. What is the value of tan 90°?

     1. -1
     2. 1
     3. Undefined ✓
     4. 0

107. 107. What is the volume of a cube with side length 5?

     1. 125 ✓
     2. 15
     3. 25
     4. 100

108. 108. What is the slope of a line parallel to a line with slope 3?

     1. -1/3
     2. 1/3
     3. -3
     4. 3 ✓

109. 109. What is the distance between points (1, 2) and (4, 6)?

     1. 7
     2. 4
     3. 3
     4. 5 ✓

110. 110. What is the x-intercept of the line y = 2x - 8?

     1. -8
     2. -4
     3. 8
     4. 4 ✓

111. 111. What is the value of cos 45°?

     1. 1/sqrt(2) ✓
     2. sqrt(3)/2
     3. 1/2
     4. 0

112. 112. If the angle of elevation of the sun is 30° and a tower casts a shadow of 20 m, what is the height of the tower (to 2 decimal places)?

     1. 10 m
     2. 20 m
     3. 17.32 m
     4. 11.55 m ✓

113. 113. What is the value of tan 45° + tan 45°?

     1. 4
     2. 0
     3. 1
     4. 2 ✓

114. 114. If the side of a cube is doubled, by what factor does its volume increase?

     1. 2
     2. 8 ✓
     3. 4
     4. 6

115. 115. Convert 2π radians to degrees.

     1. 180°
     2. 90°
     3. 360° ✓
     4. 720°

116. 116. In a right triangle, one leg is 12 and the angle adjacent to it is 60°. What is the length of the hypotenuse?

     1. 24 ✓
     2. 6
     3. 20.78
     4. 12

117. 117. A triangle with exactly two sides of equal length is called what?

     1. Scalene triangle
     2. Isosceles triangle ✓
     3. Obtuse triangle
     4. Equilateral triangle

118. 118. If a triangle has sides 5, 5, and 8, what type of triangle is it?

     1. Right
     2. Equilateral
     3. Scalene
     4. Isosceles ✓

119. 119. What is the distance between points (2, 3) and (2, 8)?

     1. 0
     2. 10
     3. 5 ✓
     4. 3

120. 120. Convert π radians to degrees.

     1. 180° ✓
     2. 270°
     3. 360°
     4. 90°

121. 121. If two tangents are drawn from an external point to a circle, what is true about their lengths?

     1. Their sum equals the diameter
     2. They are always different
     3. They are equal ✓
     4. One is always double the other

122. 122. What is the value of sec²45° - tan²45°?

     1. 2
     2. 1 ✓
     3. -1
     4. 0

123. 123. In a right triangle, if one acute angle is 40°, what is the other acute angle?

     1. 140°
     2. 40°
     3. 60°
     4. 50° ✓

124. 124. Solve for θ (0° ≤ θ ≤ 90°): sin θ = √3/2

     1. 90°
     2. 45°
     3. 60° ✓
     4. 30°

125. 125. What is the slope of the line through points (1, 2) and (3, 6)?

     1. 2 ✓
     2. 1/2
     3. 8
     4. 4

126. 126. In an isosceles triangle, the base angles are equal. If the vertex angle is 40°, what is each base angle?

     1. 60°
     2. 70° ✓
     3. 80°
     4. 50°

127. 127. Convert π/3 radians to degrees.

     1. 30°
     2. 60° ✓
     3. 90°
     4. 45°

128. 128. Convert 60° to radians.

     1. π/6
     2. 2π/3
     3. π/3 ✓
     4. π/4

129. 129. Which identity is always true for any angle θ, relating sin and cos?

     1. sinθ + cosθ = 1
     2. sin²θ - cos²θ = 1
     3. sin²θ + cos²θ = 0
     4. sin²θ + cos²θ = 1 ✓

130. 130. What is the area of a rectangle with length 8 and width 5?

     1. 26
     2. 13
     3. 40 ✓
     4. 45

131. 131. What is the value of cos 30°?

     1. sqrt(2)/2
     2. sqrt(3)/2 ✓
     3. 1
     4. 1/2

132. 132. What is the value of cos 60°?

     1. 0
     2. sqrt(3)/2
     3. 1/2 ✓
     4. 1/sqrt(2)

133. 133. What is the value of sin 60° * cos 30°?

     1. 1
     2. 3/4 ✓
     3. 1/4
     4. 1/2

134. 134. What is the value of tan 30°?

     1. 1
     2. 1/2
     3. sqrt(3)
     4. 1/sqrt(3) ✓

135. 135. A right triangle has legs of 3 and 4. What is the length of the hypotenuse?

     1. 6
     2. 4.5
     3. 5 ✓
     4. 7

136. 136. What is the midpoint of the segment joining (-2, 3) and (4, -1)?

     1. (-1, 1)
     2. (1, 1) ✓
     3. (2, 2)
     4. (1, 2)

137. 137. Solve for θ (0° ≤ θ ≤ 90°): tan θ = √3

     1. 45°
     2. 60° ✓
     3. 30°
     4. 90°

138. 138. What is the surface area of a sphere with radius 5? (Use pi ≈ 3.14; formula 4πr²)

     1. 314 ✓
     2. 157
     3. 628
     4. 78.5

139. 139. What is the term for a straight line that touches a circle at exactly one point?

     1. Secant
     2. Tangent ✓
     3. Radius
     4. Chord

140. 140. What is the term for a line segment that joins two points on a circle's circumference?

     1. Chord ✓
     2. Diameter
     3. Tangent
     4. Radius

141. 141. Convert 360° to radians.

     1. π
     2. 4π
     3. π/2
     4. 2π ✓

142. 142. What is the curved (lateral) surface area of a cylinder with radius 7 and height 10? (Use pi = 22/7)

     1. 440 ✓
     2. 220
     3. 748
     4. 308

143. 143. What is the distance between points (0, 0) and (3, 4)?

     1. 3
     2. 4
     3. 7
     4. 5 ✓

144. 144. If two triangles are similar, their corresponding sides are always what?

     1. Proportional ✓
     2. Equal
     3. Parallel only
     4. Perpendicular

145. 145. In a 45°-45°-90° triangle, if each leg is 6, what is the length of the hypotenuse?

     1. 12
     2. 6√3
     3. 6
     4. 6√2 (≈8.49) ✓

146. 146. The angle in a semicircle is always what?

     1. 60°
     2. 180°
     3. 45°
     4. 90° ✓

147. 147. In an equilateral triangle, what is the measure of each interior angle?

     1. 180°
     2. 60° ✓
     3. 90°
     4. 45°

148. 148. In a right triangle, the hypotenuse is 10 and one angle is 30°. What is the length of the side adjacent to 30°?

     1. 10
     2. 5
     3. 6
     4. 8.66 ✓

149. 149. Solve for θ (0° ≤ θ ≤ 90°): 2 sin θ = 1

     1. 60°
     2. 30° ✓
     3. 45°
     4. 90°

150. 150. What is the volume of a cube with side length 4?

     1. 64 ✓
     2. 16
     3. 48
     4. 12

151. 151. What is the value of cos 90°?

     1. 1
     2. 0 ✓
     3. 1/2
     4. Undefined

152. 152. If two lines are parallel and cut by a transversal, angles in the same relative position are called what?

     1. Corresponding angles ✓
     2. Alternate angles
     3. Complementary angles
     4. Vertical angles

153. 153. A triangle with no sides of equal length is called what?

     1. Right triangle
     2. Equilateral triangle
     3. Isosceles triangle
     4. Scalene triangle ✓

154. 154. What is the circumference of a circle with diameter 14? (Use pi = 22/7)

     1. 44 ✓
     2. 88
     3. 308
     4. 22

155. 155. In a right triangle, sine of an angle is defined as which ratio?

     1. Opposite side / Adjacent side
     2. Adjacent side / Hypotenuse
     3. Hypotenuse / Opposite side
     4. Opposite side / Hypotenuse ✓

156. 156. If the radius of a sphere is doubled, by what factor does its volume increase?

     1. 8 ✓
     2. 4
     3. 2
     4. 16

157. 157. Convert 180° to radians.

     1. π/2
     2. π/4
     3. π ✓
     4. 2π

158. 158. What is the midpoint of the segment joining (2, 4) and (6, 8)?

     1. (8, 12)
     2. (4, 4)
     3. (2, 6)
     4. (4, 6) ✓

159. 159. What is the volume of a cuboid (rectangular box) with dimensions 5, 4, and 3?

     1. 12
     2. 47
     3. 60 ✓
     4. 35

160. 160. A right triangle has legs of 9 and 12. What is the length of the hypotenuse?

     1. 21
     2. 15 ✓
     3. 18
     4. 13

161. 161. Find the midpoint of the segment joining (1, 1) and (7, 9).

     1. (3, 4)
     2. (6, 8)
     3. (8, 10)
     4. (4, 5) ✓

162. 162. What is the distance between points (3, -2) and (7, 1)?

     1. 7
     2. 4
     3. 3
     4. 5 ✓

163. 163. Two triangles are similar if their corresponding angles are what?

     1. Supplementary
     2. Complementary
     3. Different
     4. Equal ✓

164. 164. A right triangle has a hypotenuse of 13 and one leg of 5. What is the length of the other leg?

     1. 12 ✓
     2. 14
     3. 10
     4. 8

165. 165. What is the slope-intercept equation of a line with slope 2 passing through (0, 3)?

     1. y = 2x - 3
     2. y = 2x + 3 ✓
     3. y = -2x + 3
     4. y = 3x + 2

166. 166. sin θ / cos θ is equal to which trig function?

     1. sec θ
     2. cot θ
     3. csc θ
     4. tan θ ✓

167. 167. Two angles that add up to 90° are called what?

     1. Adjacent angles
     2. Supplementary angles
     3. Complementary angles ✓
     4. Vertical angles

168. 168. What is the term for a region bounded by an arc and the two radii joining its endpoints to the center?

     1. Chord
     2. Sector ✓
     3. Tangent
     4. Segment

169. 169. A pole 6 m high casts a shadow 6 m long. What is the angle of elevation of the sun?

     1. 60°
     2. 45° ✓
     3. 90°
     4. 30°

170. 170. What is the circumference of a circle with radius 7? (Use pi = 22/7)

     1. 22
     2. 88
     3. 44 ✓
     4. 154

171. 171. What is the value of cos 0°?

     1. 1/2
     2. 1 ✓
     3. 0
     4. Undefined

172. 172. What is the value of tan 60°?

     1. sqrt(3) ✓
     2. 1/sqrt(3)
     3. 0
     4. 1

173. 173. What is the value of sin 90°?

     1. 1 ✓
     2. Undefined
     3. 0
     4. 1/2

174. 174. A ladder reaches a height of 24 m when placed against a wall at an angle such that its base is 7 m from the wall. What is the length of the ladder?

     1. 26 m
     2. 31 m
     3. 24 m
     4. 25 m ✓

175. 175. In a right triangle, the hypotenuse is 20 and one angle is 60°. What is the length of the side opposite to 60°?

     1. 17.32 ✓
     2. 14.14
     3. 10
     4. 20

176. 176. In a triangle, if two angles measure 50° and 60°, what is the third angle?

     1. 60°
     2. 80°
     3. 70° ✓
     4. 50°

177. 177. What is the y-intercept of the line y = 4x - 7?

     1. -7 ✓
     2. 7
     3. -4
     4. 4

178. 178. In a 45°-45°-90° triangle, if the hypotenuse is 10, what is the length of each leg?

     1. 5√2 (≈7.07) ✓
     2. 5
     3. 7.5
     4. 10

179. 179. A right triangle has legs of 5 and 12. What is the length of the hypotenuse?

     1. 17
     2. 11
     3. 15
     4. 13 ✓

180. 180. What is the value of sin 0°?

     1. 1/2
     2. 0 ✓
     3. Undefined
     4. 1

181. 181. What is the reciprocal of tangent called?

     1. Cosecant
     2. Secant
     3. Cotangent ✓
     4. Sine

182. 182. Opposite angles of a cyclic quadrilateral (inscribed in a circle) always add up to what?

     1. 270°
     2. 180° ✓
     3. 90°
     4. 360°

183. 183. What is the area of a trapezoid with parallel sides 8 and 12, and height 5?

     1. 50 ✓
     2. 48
     3. 100
     4. 40

184. 184. Which identity is always true for any angle θ, relating cot and csc?

     1. 1 + cot²θ = sec²θ
     2. 1 + cot²θ = csc²θ ✓
     3. 1 - cot²θ = csc²θ
     4. cot²θ - 1 = csc²θ

185. 185. What is the equation of a line with slope 0 passing through (2, 5)?

     1. y = 5 ✓
     2. y = 2
     3. x = 2
     4. x = 5

186. 186. Convert π/2 radians to degrees.

     1. 60°
     2. 180°
     3. 45°
     4. 90° ✓

187. 187. A cube has a volume of 27 cubic units. What is the length of one side?

     1. 9
     2. 27
     3. 6
     4. 3 ✓

188. 188. What is the radius of a circle with diameter 24?

     1. 48
     2. 12 ✓
     3. 6
     4. 24

189. 189. What is the slope of the line through points (2, 5) and (2, 9)?

     1. Undefined ✓
     2. 0
     3. 4
     4. 1

190. 190. What type of angle measures less than 90°?

     1. Obtuse angle
     2. Acute angle ✓
     3. Right angle
     4. Reflex angle

191. 191. What is the area of a rhombus with diagonals 6 and 8?

     1. 48
     2. 24 ✓
     3. 28
     4. 14

192. 192. What is the sum of the interior angles of a quadrilateral?

     1. 270°
     2. 180°
     3. 540°
     4. 360° ✓

193. 193. What is the surface area of a cube with side length 4?

     1. 96 ✓
     2. 48
     3. 16
     4. 64

194. 194. The area of a right triangle with legs 6 and 8 is:

     1. 24 ✓
     2. 48
     3. 14
     4. 20

195. 195. A triangle has sides 6, 6, and 6. What type of triangle is it (in terms of angles)?

     1. Right
     2. Obtuse
     3. Scalene
     4. Equilateral, and also acute ✓

196. 196. A triangle with all three sides of equal length is called what?

     1. Equilateral triangle ✓
     2. Scalene triangle
     3. Isosceles triangle
     4. Right triangle

197. 197. cos θ / sin θ is equal to which trig function?

     1. tan θ
     2. csc θ
     3. sec θ
     4. cot θ ✓

198. 198. A right triangle has a hypotenuse of 10 and one leg of 6. What is the length of the other leg?

     1. 6
     2. 8 ✓
     3. 12
     4. 10

199. 199. If two triangles are congruent, which of the following is true?

     1. They must be right triangles
     2. Only their perimeters are equal
     3. Only their areas are equal
     4. Their corresponding sides and angles are all equal ✓

200. 200. Using Heron's formula, find the area of a triangle with sides 5, 5, and 6.

     1. 24
     2. 12 ✓
     3. 15
     4. 10