Bluebook SAT Test Right Triangles and Trigonometry 3

Question 1

In right triangle MNO with the right angle at O, MN = 10 and MO = 6. What is cos(M)?

Accepted Answer

3/5

Answer

cos(M) = adjacent/hypotenuse = MO/MN = 6/10 = 3/5.

Question 2

A tree casts a shadow 24 feet long. A 6-foot person standing nearby casts a shadow 4 feet long. How tall is the tree?

Accepted Answer

36

Answer

Similar triangles: tree/24 = 6/4; tree = 6 × 24/4 = 36.

Question 3

In a 30-60-90 triangle, the hypotenuse is 16. What is the length of the longer leg?

Accepted Answer

8√3

Answer

Shorter leg = 16/2 = 8; longer leg = 8√3.

Question 4

From the top of a 40-foot cliff, the angle of depression to a boat is 30°. How far is the boat from the base of the cliff?

Accepted Answer

40√3

Answer

tan(30°) = 40/d; d = 40/tan(30°) = 40/(1/√3) = 40√3.

Question 5

A right triangle has legs x and x + 7. Its hypotenuse is 13. What is the smaller leg x?

Accepted Answer

5

Answer

x² + (x+7)² = 169 → 2x² + 14x + 49 = 169 → 2x² + 14x − 120 = 0 → x² + 7x − 60 = 0 → (x+12)(x−5) = 0; x = 5.

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