Right Triangles and Trigonometry Flashcards

In right triangle PQR with right angle at R, PQ = 29 and PR = 20. What is QR?

Answer: 21

QR = √(29² − 20²) = √(841 − 400) = √441 = 21.

In right triangle ABC with right angle at C, sin(B) = 7/25. What is cos(B)?

Answer: 24/25

cos(B) = √(1 − 49/625) = √(576/625) = 24/25.

A surveyor stands 80 feet from the base of a tower. The angle of elevation to the top of the tower is 45°. How tall is the tower?

Answer: 80

tan(45°) = 1 = height/80; height = 80.

A right triangle has legs of length 3k and 4k. If the hypotenuse is 50, what is k?

Answer: 10

(3k)² + (4k)² = 25k² = 2500; k² = 100; k = 10.

In a 45-45-90 triangle, angle A = 45° and the side opposite A is 6√2. What is the hypotenuse?

Answer: 12

In a 45-45-90 triangle both legs are equal and the hypotenuse = leg × √2; leg = 6√2, so hyp = 6√2 × √2 = 12.

Right triangles P and Q are similar. Triangle P has legs 8 and 15. Triangle Q has the longer leg equal to 45. What is the hypotenuse of Triangle Q?

Answer: 51

Scale factor = 45/15 = 3; Triangle P hypotenuse = 17; Triangle Q hypotenuse = 17 × 3 = 51.

In right triangle ABC with right angle at C, angle A = 60° and AC = 5. What is BC?

Answer: 5√3

tan(60°) = √3 = BC/AC = BC/5; BC = 5√3.