Bluebook SAT Test Right Triangles and Trigonometry 9

Question 1

In right triangle ABC with the right angle at C, if sin(A) = 2/3, what is the value of sin²(A) + cos²(A)?

Accepted Answer

1

Answer

The Pythagorean identity states sin²(θ) + cos²(θ) = 1 for any angle θ.

Question 2

A right triangle has legs of length 7 and 24. What is the value of sin of the angle opposite the leg of length 7?

Accepted Answer

7/25

Answer

The hypotenuse is √(7² + 24²) = √(49 + 576) = √625 = 25, so sin = opposite/hypotenuse = 7/25.

Question 3

In a 30-60-90 right triangle, if the hypotenuse has length 8, what is the length of the side opposite the 60° angle?

Accepted Answer

4√3

Answer

In a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2, so the side opposite 60° = (8/2)·√3 = 4√3.

Question 4

Right triangle PQR has the right angle at R. If cos(P) = 5/13, what is tan(P)?

Accepted Answer

12/5

Answer

If cos(P) = 5/13, then the adjacent leg is 5 and hypotenuse is 13, so the opposite leg is √(169 − 25) = 12, giving tan(P) = 12/5.

Question 5

A 10-foot ladder leans against a vertical wall. The base of the ladder is 6 feet from the wall. At what angle, to the nearest degree, does the ladder make with the ground?

Accepted Answer

53°

Answer

cos(θ) = 6/10 = 0.6, so θ = cos⁻¹(0.6) ≈ 53°.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Right Triangles and Trigonometry 9