Bluebook SAT Test Right Triangles and Trigonometry 10

Question 1

In right triangle XYZ with right angle at Z, XZ = 8 and XY = 17. What is cos(X)?

Accepted Answer

8/17

Answer

XZ = 8 is adjacent to X and XY = 17 is the hypotenuse, so cos(X) = adjacent/hypotenuse = 8/17.

Question 2

A surveyor looks up at the top of a flagpole. The angle of elevation is 30° and the surveyor is 45 feet from the base. How tall is the flagpole?

Accepted Answer

15√3

Answer

tan(30°) = height/45, so height = 45·tan(30°) = 45·(1/√3) = 45/√3 = 45√3/3 = 15√3.

Question 3

A right triangle has a hypotenuse of 13 and one leg of 5. What is the sine of the larger acute angle?

Accepted Answer

12/13

Answer

The other leg = √(169 − 25) = 12. The larger acute angle is opposite the longer leg (12), so sin = 12/13.

Question 4

In a 45-45-90 right triangle, if one leg has length 5, what is the length of the hypotenuse?

Accepted Answer

5√2

Answer

In a 45-45-90 triangle, hypotenuse = leg × √2 = 5√2.

Question 5

Right triangle DEF has right angle at E. If tan(D) = 3 and EF = 6, what is DF?

Accepted Answer

2√10

Answer

tan(D) = EF/DE = 6/DE = 3, so DE = 2. Then DF = √(DE² + EF²) = √(4 + 36) = √40 = 2√10.

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