Bluebook SAT Test Geometry and Trigonometry

Question 1

A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?

Accepted Answer

10

Answer

By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = 10.

Question 2

The area of a circle with radius 5 is closest to which value? (Use π ≈ 3.14)

Accepted Answer

78.5

Answer

Area = πr² = 3.14 × 25 = 78.5.

Question 3

Two angles of a triangle measure 55° and 75°. What is the measure of the third angle?

Accepted Answer

50°

Answer

Sum of angles in a triangle = 180°. Third angle = 180 − 55 − 75 = 50°.

Question 4

In a right triangle, sin(θ) = 3/5. What is cos(θ)?

Accepted Answer

4/5

Answer

sin²(θ) + cos²(θ) = 1. cos²(θ) = 1 − 9/25 = 16/25. cos(θ) = 4/5.

Question 5

A rectangle has a length of 12 and a width of 7. What is its perimeter?

Accepted Answer

38

Answer

Perimeter = 2(l + w) = 2(12 + 7) = 2(19) = 38.

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