Geometry Trigonometry & Applications 2 — Questions and Answers
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?
- 30 tan 40° (Correct answer)
- 30 sin 40°
- 30 cos 40°
- 30 / tan 40°
Correct answer: 30 tan 40°
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°?
- 1/2 (Correct answer)
- √3/2
- √2/2
- 1
Correct answer: 1/2
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?
- 10 sin 60° ≈ 8.66 ft (Correct answer)
- 10 cos 60° = 5 ft
- 10 tan 60° ≈ 17.3 ft
- 10 / sin 60° ≈ 11.5 ft
Correct answer: 10 sin 60° ≈ 8.66 ft
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?
- 4/5 (Correct answer)
- 3/4
- 5/3
- 5/4
Correct answer: 4/5
A 3-4-5 triangle gives opposite 4 and hypotenuse 5, so sin θ = 4/5.
Question 5: Which trigonometric ratio equals opposite/adjacent?
- Tangent (Correct answer)
- Sine
- Cosine
- Secant
Correct answer: Tangent
Tangent is defined as the ratio of the opposite side to the adjacent side.
Question 6: The angle of depression from a 50 ft cliff to a boat is 25°. How far is the boat from the base of the cliff?
- 50 / tan 25° ≈ 107 ft (Correct answer)
- 50 tan 25° ≈ 23 ft
- 50 sin 25° ≈ 21 ft
- 50 cos 25° ≈ 45 ft
Correct answer: 50 / tan 25° ≈ 107 ft
tan 25° = 50/distance, so distance = 50/tan 25° ≈ 107 ft.
Question 7: What is tan 45°?
- 1 (Correct answer)
- 0
- √3
- 1/2
Correct answer: 1
In a 45-45-90 triangle the legs are equal, so tan 45° = 1.
Geometry Trigonometry & Applications 2
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?