Right Triangles and Trigonometry Flashcards

In right triangle XYZ with right angle at Z, XZ = 8 and XY = 17. What is cos(X)?

Answer: 8/17

XZ = 8 is adjacent to X and XY = 17 is the hypotenuse, so cos(X) = adjacent/hypotenuse = 8/17.

A surveyor looks up at the top of a flagpole. The angle of elevation is 30° and the surveyor is 45 feet from the base. How tall is the flagpole?

Answer: 15√3

tan(30°) = height/45, so height = 45·tan(30°) = 45·(1/√3) = 45/√3 = 45√3/3 = 15√3.

A right triangle has a hypotenuse of 13 and one leg of 5. What is the sine of the larger acute angle?

Answer: 12/13

The other leg = √(169 − 25) = 12. The larger acute angle is opposite the longer leg (12), so sin = 12/13.

In a 45-45-90 right triangle, if one leg has length 5, what is the length of the hypotenuse?

Answer: 5√2

In a 45-45-90 triangle, hypotenuse = leg × √2 = 5√2.

Right triangle DEF has right angle at E. If tan(D) = 3 and EF = 6, what is DF?

Answer: 2√10

tan(D) = EF/DE = 6/DE = 3, so DE = 2. Then DF = √(DE² + EF²) = √(4 + 36) = √40 = 2√10.

In right triangle ABC with right angle at C, angle A = 30° and AB = 12. What is the length of BC?

Answer: 6

sin(30°) = BC/AB = BC/12, so BC = 12 × sin(30°) = 12 × 0.5 = 6.

In right triangle PQR with the right angle at R, PQ = 29 and QR = 21. What is sin(Q)?

Answer: 20/29

PR = √(PQ² − QR²) = √(841 − 441) = √400 = 20. sin(Q) = PR/PQ = 20/29.