NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3 — Questions and Answers
Question 1: Calculate the exact value of tan(45°):
- 0
- 1/√2
- √3
- 1 (Correct answer)
Correct answer: 1
tan(45°) = sin(45°) / cos(45°) = (1/√2) / (1/√2) = 1.
Question 2: A ladder 10 m long leans against a wall, making an angle of 60° with the ground. How high up the wall does the ladder reach?
- 5 m
- 5√2 m
- 5√3 m (Correct answer)
- 10√3 m
Correct answer: 5√3 m
Height = 10 × sin(60°) = 10 × (√3/2) = 5√3 m.
Question 3: The exterior angle of a regular polygon is 36°. How many sides does the polygon have?
- 8
- 9
- 10 (Correct answer)
- 12
Correct answer: 10
The sum of exterior angles of any polygon = 360°. Number of sides = 360° ÷ 36° = 10 sides.
Question 4: In the unit circle, what are the coordinates of the point at 270°?
- (0, 1)
- (1, 0)
- (0, -1) (Correct answer)
- (-1, 0)
Correct answer: (0, -1)
At 270°, the point is directly at the bottom of the unit circle: (cos 270°, sin 270°) = (0, -1).
Question 5: A right triangle has legs of length a and b, and hypotenuse c. Which identity correctly expresses the cosine of the angle opposite the leg of length a?
- cos θ = a/c
- cos θ = b/c (Correct answer)
- cos θ = a/b
- cos θ = c/a
Correct answer: cos θ = b/c
cos θ = adjacent/hypotenuse. The side adjacent to angle θ (which is opposite leg a) is leg b. So cos θ = b/c.
Question 6: The volume of a cone is given by V = (1/3)πr²h. A cone has radius 6 cm and height 9 cm. What is its volume? (Use π ≈ 3.14)
- 254.3 cm³
- 324.1 cm³
- 339.12 cm³ (Correct answer)
- 376.8 cm³
Correct answer: 339.12 cm³
V = (1/3) × 3.14 × 6² × 9 = (1/3) × 3.14 × 36 × 9 = (1/3) × 1017.36 = 339.12 cm³.
NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3
Calculate the exact value of tan(45°):