Right Triangles and Trigonometry Flashcards

In right triangle ABC with the right angle at C, tan(A) = 7/24. What is the length of the hypotenuse if AC = 24?

Answer: 25

tan(A) = BC/AC = 7/24, so BC = 7; hyp = √(7² + 24²) = √(49 + 576) = √625 = 25.

A 45-45-90 triangle has a perimeter of 20 + 10√2. What is the length of the hypotenuse?

Answer: 10√2

Let each leg = a; perimeter = 2a + a√2 = a(2 + √2) = 20 + 10√2 = 10(2 + √2); so a = 10 and hyp = 10√2.

In right triangle RST with right angle at T, RS = 15 and RT = 9. What is sin(R)?

Answer: 4/5

ST = √(15² − 9²) = √(225 − 81) = √144 = 12; sin(R) = ST/RS = 12/15 = 4/5.

From a point on level ground, the angle of elevation to the top of a 60-meter building is 45°. How far is the point from the base of the building?

Answer: 60

tan(45°) = 1 = 60/d; d = 60.

A right triangle has a hypotenuse of 2 and one leg of √3. What is the measure of the smallest angle?

Answer: 30°

Other leg = √(4 − 3) = 1; the triangle has sides 1, √3, 2 — a 30-60-90 triangle; smallest angle = 30°.

In similar right triangles, the ratio of the shorter legs is 3:7. If the area of the smaller triangle is 27 square units, what is the area of the larger triangle?

Answer: 147

Area scales as the square of the linear ratio: (7/3)² × 27 = 49/9 × 27 = 147.

In right triangle ABC with right angle at C, cos(A) = 12/13. What is tan(A)?

Answer: 5/12

sin(A) = √(1 − 144/169) = 5/13; tan(A) = sin/cos = (5/13)/(12/13) = 5/12.