Bluebook SAT Test Right Triangles and Trigonometry 7

Question 1

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

Accepted Answer

12

Answer

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

Question 2

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

Accepted Answer

81

Answer

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

Question 3

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?

Accepted Answer

100

Answer

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

Question 4

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

Accepted Answer

10

Answer

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

Question 5

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

Accepted Answer

10 sin(37°)

Answer

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

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