NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3

Question 1

Calculate the exact value of tan(45°):

Accepted Answer

1

Answer

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?

Accepted Answer

5√3 m

Answer

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?

Accepted Answer

10

Answer

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°?

Accepted Answer

(0, -1)

Answer

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?

Accepted Answer

cos θ = b/c

Answer

cos θ = adjacent/hypotenuse. The side adjacent to angle θ (which is opposite leg a) is leg b. So cos θ = b/c.

(NBT) National Benchmark Test Practice Test

(NBT) National Benchmark Test Practice Test

NBT - National Benchmark Mathematics: Geometry and Trigonometry Questions and Answers 3