Geometry Trigonometry & Applications 2

Question 1

In a right triangle, the angle of elevation to the top of a tree from a point 30 ft away is 40°. Which expression gives the tree's height?

Accepted Answer

30 tan 40°

Answer

Height is the opposite side, so tan 40° = height/30, giving height = 30 tan 40°.

Question 2

What is the exact value of sin 30°?

Accepted Answer

1/2

Answer

sin 30° equals 1/2 from the standard 30-60-90 triangle.

Question 3

A 10 ft ladder leans against a wall making a 60° angle with the ground. How high up the wall does it reach?

Accepted Answer

10 sin 60° ≈ 8.66 ft

Answer

The wall height is opposite the 60° angle, so height = 10 sin 60° ≈ 8.66 ft.

Question 4

If cos θ = 3/5 in a right triangle, what is sin θ?

Accepted Answer

4/5

Answer

A 3-4-5 triangle gives opposite 4 and hypotenuse 5, so sin θ = 4/5.

Question 5

Which trigonometric ratio equals opposite/adjacent?

Accepted Answer

Tangent

Answer

Tangent is defined as the ratio of the opposite side to the adjacent side.

Geometry Practice Test