Trigonometry & Applications Flashcards
7 cards from real Geometry practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Trigonometry & Applications flashcards as text
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?
Answer: 30 tan 40°
Height is the opposite side, so tan 40° = height/30, giving height = 30 tan 40°.
What is the exact value of sin 30°?
Answer: 1/2
sin 30° equals 1/2 from the standard 30-60-90 triangle.
A 10 ft ladder leans against a wall making a 60° angle with the ground. How high up the wall does it reach?
Answer: 10 sin 60° ≈ 8.66 ft
The wall height is opposite the 60° angle, so height = 10 sin 60° ≈ 8.66 ft.
If cos θ = 3/5 in a right triangle, what is sin θ?
Answer: 4/5
A 3-4-5 triangle gives opposite 4 and hypotenuse 5, so sin θ = 4/5.
Which trigonometric ratio equals opposite/adjacent?
Answer: Tangent
Tangent is defined as the ratio of the opposite side to the adjacent side.
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?
Answer: 50 / tan 25° ≈ 107 ft
tan 25° = 50/distance, so distance = 50/tan 25° ≈ 107 ft.
What is tan 45°?
Answer: 1
In a 45-45-90 triangle the legs are equal, so tan 45° = 1.