Right Triangles and Trigonometry Flashcards

In right triangle ABC with right angle at C, AB = 20 and sin(A) = 3/5. What is BC?

Answer: 12

sin(A) = BC/AB = BC/20 = 3/5; BC = 12.

A right isosceles triangle has a hypotenuse of 18. What is the area of the triangle?

Answer: 81

Legs = 18/√2 = 9√2; area = (1/2)(9√2)(9√2) = (1/2)(162) = 81.

From the base of a hill, a climber walks 200 meters along a slope that makes a 30° angle with the horizontal. How high does the climber rise?

Answer: 100

Height = 200 sin(30°) = 200 × 1/2 = 100.

In right triangle JKL with right angle at L, tan(K) = 2. If KL = 5, what is JL?

Answer: 10

tan(K) = JL/KL = JL/5 = 2; JL = 10.

A right triangle has a hypotenuse of 10 and one acute angle of 37°. Which expression gives the leg opposite the 37° angle?

Answer: 10 sin(37°)

sin(37°) = opposite/hypotenuse; opposite = 10 sin(37°).

Two right triangles share the same hypotenuse of length 26. One has a leg of 10; the other has a leg of 24. Are both valid right triangles?

Answer: Yes — 10-24-26 and both satisfy the Pythagorean theorem

10² + 24² = 100 + 576 = 676 = 26²; both 10-24-26 (same triangle, just different legs named) satisfy the theorem.

A 30-60-90 triangle has hypotenuse 22. What is the area of the triangle?

Answer: (121√3)/2

Short leg = 11; long leg = 11√3; area = (1/2)(11)(11√3) = (121√3)/2.