Bluebook SAT Test Right Triangles and Trigonometry 4

Question 1

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

Accepted Answer

25

Answer

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

Question 2

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

Accepted Answer

10√2

Answer

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

Question 3

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

Accepted Answer

4/5

Answer

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

Question 4

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?

Accepted Answer

60

Answer

tan(45°) = 1 = 60/d; d = 60.

Question 5

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

Accepted Answer

30°

Answer

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

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