Bluebook SAT Test Right Triangles and Trigonometry 11

Question 1

In right triangle ABC with right angle at C, if sin(A) = k, what is cos(B)?

Accepted Answer

k

Answer

Angles A and B are complementary (sum to 90°), so cos(B) = cos(90° − A) = sin(A) = k.

Question 2

A right triangle has a leg of 15 and a hypotenuse of 17. What is the area of the triangle?

Accepted Answer

60

Answer

The other leg = √(289 − 225) = √64 = 8. Area = (1/2)(15)(8) = 60.

Question 3

From a window 40 feet above the ground, the angle of depression to a car parked on the street is 45°. How far is the car from the building (horizontal distance)?

Accepted Answer

40 feet

Answer

The angle of depression equals the angle of elevation from the car. tan(45°) = 40/d, so d = 40.

Question 4

In a right triangle, the ratio of the two legs is 1:√3. Which of the following describes the acute angles?

Accepted Answer

30° and 60°

Answer

A ratio of legs 1:√3 matches the 30-60-90 triangle, where the opposite sides are in ratio 1:√3:2.

Question 5

In right triangle RST with right angle at S, RS = a and ST = b. Which expression gives sin(T)?

Accepted Answer

a/√(a²+b²)

Answer

The hypotenuse RT = √(a²+b²). sin(T) = opposite/hypotenuse = RS/RT = a/√(a²+b²).

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Right Triangles and Trigonometry 11