Bluebook SAT Test Right Triangles and Trigonometry 6

Question 1

A right triangle has legs of 20 and 21. What is the length of the hypotenuse?

Accepted Answer

29

Answer

c = √(20² + 21²) = √(400 + 441) = √841 = 29.

Question 2

In right triangle ABC with right angle at C, sin(A) = 5/13. What is the length of AC if AB = 26?

Accepted Answer

24

Answer

BC/AB = 5/13; BC = 10; AC = √(26² − 10²) = √(676 − 100) = √576 = 24.

Question 3

An observer stands 50 meters from a building. The angle of elevation to the roof is 60°. How tall is the building?

Accepted Answer

50√3

Answer

tan(60°) = √3 = height/50; height = 50√3.

Question 4

A 30-60-90 triangle has the longer leg = 12. What is the hypotenuse?

Accepted Answer

8√3

Answer

Shorter leg = 12/√3 = 4√3; hypotenuse = 2 × 4√3 = 8√3.

Question 5

In right triangle GHI with right angle at H, GH = 8 and GI = 17. What is cos(G)?

Accepted Answer

8/17

Answer

cos(G) = adjacent/hypotenuse = GH/GI = 8/17.

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