Bluebook SAT Test Right Triangles and Trigonometry 14

Question 1

An airplane climbs at an angle of 15° from the horizontal. After traveling 4,000 feet along the flight path, how high has it climbed? (Use sin 15° ≈ 0.259)

Accepted Answer

1,036 feet

Answer

Height = 4000 × sin(15°) = 4000 × 0.259 = 1,036 feet.

Question 2

In right triangle ABC with right angle at C, the ratio BC : AC = 3 : 4. Which is the value of sin(A)?

Accepted Answer

3/5

Answer

With BC = 3k and AC = 4k, the hypotenuse AB = 5k. sin(A) = BC/AB = 3k/5k = 3/5.

Question 3

Two similar right triangles have perimeters 18 and 30. The smaller triangle has a hypotenuse of 8. What is the hypotenuse of the larger triangle?

Accepted Answer

40/3

Answer

Scale factor = 30/18 = 5/3. Larger hypotenuse = 8 × (5/3) = 40/3.

Question 4

In right triangle XYZ with right angle at Z, if sin(X) = a/b, what is the length of YZ in terms of a, b, and XY?

Accepted Answer

a·XY/b

Answer

sin(X) = YZ/XY = a/b, so YZ = a·XY/b.

Question 5

A right triangle has legs in ratio 5:12. If the hypotenuse is 26, what is the shorter leg?

Accepted Answer

10

Answer

The legs are 5k and 12k; hypotenuse = 13k = 26, so k = 2. Shorter leg = 5k = 10.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Right Triangles and Trigonometry 14