Bluebook SAT Test Right Triangles and Trigonometry 5

Question 1

In right triangle XYZ with right angle at Z, XY = 25 and YZ = 7. What is cos(Y)?

Accepted Answer

7/25

Answer

cos(Y) = adjacent/hypotenuse = YZ/XY = 7/25.

Question 2

A 30-60-90 triangle has the longer leg equal to 9√3. What is the length of the shorter leg?

Accepted Answer

9

Answer

Longer leg = short leg × √3 = 9√3; short leg = 9.

Question 3

A wire is attached from the top of a 30-foot pole to a stake 16 feet from the base. How long is the wire?

Accepted Answer

34

Answer

Wire² = 30² + 16² = 900 + 256 = 1156; wire = 34.

Question 4

In right triangle DEF with right angle at F, tan(D) = 3/4 and EF = 9. What is DE?

Accepted Answer

15

Answer

tan(D) = EF/DF = 9/DF = 3/4; DF = 12; DE = √(9² + 12²) = √225 = 15.

Question 5

Two right triangles are similar. Their areas are 50 and 200 square units. What is the ratio of their corresponding sides?

Accepted Answer

1:2

Answer

Area ratio = 50:200 = 1:4; side ratio = √(1/4) = 1:2.

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