Right Triangles and Trigonometry Flashcards

A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?

Answer: 15

By the Pythagorean theorem: c² = 9² + 12² = 81 + 144 = 225, so c = 15.

In right triangle ABC with the right angle at C, sin(A) = 3/5. What is cos(A)?

Answer: 4/5

Since sin²(A) + cos²(A) = 1: cos(A) = √(1 − 9/25) = √(16/25) = 4/5.

A 30-60-90 triangle has the shortest leg equal to 7. What is the length of the hypotenuse?

Answer: 14

In a 30-60-90 triangle the hypotenuse is twice the shortest leg: 2 × 7 = 14.

In right triangle PQR with the right angle at R, tan(P) = 5/12. If QR = 5, what is PR?

Answer: 12

tan(P) = opposite/adjacent = QR/PR = 5/PR; solving, PR = 5 × 12/5 = 12.

A ladder leans against a wall, making a 60° angle with the ground. If the ladder is 20 feet long, how high on the wall does it reach?

Answer: 10√3

Height = 20 sin(60°) = 20 × (√3/2) = 10√3.

A 45-45-90 triangle has a hypotenuse of 10√2. What is the length of each leg?

Answer: 10

In a 45-45-90 triangle, leg = hypotenuse/√2 = 10√2/√2 = 10.

In right triangle DEF with the right angle at F, DE = 13 and EF = 5. What is sin(E)?

Answer: 12/13

DF = √(13² − 5²) = √(169 − 25) = √144 = 12; sin(E) = opposite/hypotenuse = DF/DE = 12/13.