Bluebook SAT Test Right Triangles and Trigonometry 15

Question 1

In right triangle ABC with right angle at C, sin(A) = 2√5/5. What is tan(A)?

Accepted Answer

2

Answer

sin(A) = 2√5/5, so opposite = 2√5 and hypotenuse = 5. Adjacent = √(25 − 20) = √5. tan(A) = 2√5/√5 = 2.

Question 2

A 45-45-90 triangle has area 72. What is the perimeter?

Accepted Answer

24 + 12√2

Answer

Area = (1/2)s² = 72 so s = 12. Hypotenuse = 12√2. Perimeter = 12 + 12 + 12√2 = 24 + 12√2.

Question 3

In right triangle PQR with right angle at R, if cos(P) = x, what is tan(Q)?

Accepted Answer

x/√(1−x²)

Answer

Angles P and Q are complementary, so sin(Q) = cos(P) = x and cos(Q) = sin(P) = √(1−x²). Thus tan(Q) = sin(Q)/cos(Q) = x/√(1−x²).

Question 4

A vertical pole casts a shadow 20 feet long. The sun's rays make a 60° angle with the ground. How tall is the pole?

Accepted Answer

20√3

Answer

tan(60°) = height/20, so height = 20·tan(60°) = 20√3.

Question 5

In right triangle ABC, the right angle is at C. If BC = 7 and angle A = 45°, what is AB?

Accepted Answer

7√2

Answer

sin(45°) = BC/AB = 7/AB, so AB = 7/sin(45°) = 7/(√2/2) = 7·2/√2 = 14/√2 = 7√2.

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