Bluebook SAT Test Right Triangles and Trigonometry 16

Question 1

In right triangle ABC with right angle at C, if the hypotenuse AB = √5 and one leg AC = 1, what is tan(B)?

Accepted Answer

1/2

Answer

BC = √(5−1) = 2. Opposite to angle B is AC = 1; adjacent to B is BC = 2. So tan(B) = 1/2.

Question 2

A right triangle has legs a and b with a > b. The angle opposite b is 30°. Which of the following must be true?

Accepted Answer

All of the above

Answer

In a 30-60-90 triangle, if b is opposite 30° and a is opposite 60°, then a = b√3. This means b = a/√3 and a/b = √3, so all three are equivalent.

Question 3

The hypotenuse of a right triangle lies along the x-axis from (0,0) to (10,0). The right angle vertex is at (6, y) with y > 0. What is y?

Accepted Answer

2√6

Answer

In a right triangle inscribed in a semicircle, the altitude from the right angle to the hypotenuse = √(product of the two segments). Segments are 6 and 4, so y = √(6 × 4) = √24 = 2√6.

Question 4

In right triangle MNP with right angle at N, MP = 2 and sin(M) = sin(P). What is the area of the triangle?

Accepted Answer

1

Answer

sin(M) = sin(P) implies M = P = 45° (both acute in a right triangle). So it's a 45-45-90 triangle with hypotenuse 2. Each leg = 2/√2 = √2. Area = (1/2)(√2)(√2) = 1.

Question 5

In right triangle RST with right angle at T, RT = 5 and RS = 13. What is the value of (sin R)(cos R)?

Accepted Answer

60/169

Answer

ST = √(169−25) = 12. sin(R) = ST/RS = 12/13; cos(R) = RT/RS = 5/13. Product = (12/13)(5/13) = 60/169.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Right Triangles and Trigonometry 16