Bluebook SAT Test Geometry and Trigonometry 1 — Questions and Answers
Question 1: A right triangle has legs of length 6 and 8. What is the length of the hypotenuse?
- 10 (Correct answer)
- 12
- 14
- 7
Correct answer: 10
By the Pythagorean theorem: c² = 6² + 8² = 36 + 64 = 100, so c = 10.
Using the Pythagorean theorem, c² = a² + b² = 6² + 8² = 36 + 64 = 100. Taking the square root: c = √100 = 10. This is the classic 6-8-10 right triangle (a multiple of the 3-4-5 triple).
Question 2: The area of a circle with radius 5 is closest to which value? (Use π ≈ 3.14)
- 15.7
- 31.4
- 78.5 (Correct answer)
- 157
Correct answer: 78.5
Area = πr² = 3.14 × 25 = 78.5.
The area of a circle is A = πr². With r = 5 and π ≈ 3.14: A = 3.14 × 5² = 3.14 × 25 = 78.5 square units.
Question 3: Two angles of a triangle measure 55° and 75°. What is the measure of the third angle?
- 40°
- 50° (Correct answer)
- 60°
- 70°
Correct answer: 50°
Sum of angles in a triangle = 180°. Third angle = 180 − 55 − 75 = 50°.
The sum of interior angles in a triangle is always 180°. The third angle = 180° − 55° − 75° = 180° − 130° = 50°.
Question 4: In a right triangle, sin(θ) = 3/5. What is cos(θ)?
- 3/4
- 4/5 (Correct answer)
- 5/3
- 4/3
Correct answer: 4/5
sin²(θ) + cos²(θ) = 1. cos²(θ) = 1 − 9/25 = 16/25. cos(θ) = 4/5.
Using the Pythagorean identity: sin²(θ) + cos²(θ) = 1. So cos²(θ) = 1 − (3/5)² = 1 − 9/25 = 16/25. Therefore cos(θ) = 4/5 (positive since θ is an acute angle in a right triangle).
Question 5: A rectangle has a length of 12 and a width of 7. What is its perimeter?
- 19
- 38 (Correct answer)
- 84
- 76
Correct answer: 38
Perimeter = 2(l + w) = 2(12 + 7) = 2(19) = 38.
The perimeter of a rectangle is P = 2(l + w) = 2(12 + 7) = 2(19) = 38. Note: the area would be l × w = 84, which is a common distractor.
Question 6: A circle has a circumference of 20π. What is its radius?
- 5
- 10 (Correct answer)
- 20
- 40
Correct answer: 10
C = 2πr → 20π = 2πr → r = 10.
The circumference of a circle is C = 2πr. Given C = 20π: 20π = 2πr. Dividing both sides by 2π: r = 10.
Question 7: In a right triangle, the angle opposite the hypotenuse is:
- 45°
- 60°
- 90° (Correct answer)
- 30°
Correct answer: 90°
By definition, a right triangle contains one 90° angle, and the side opposite to it is the hypotenuse.
A right triangle is defined as a triangle that contains one right angle (90°). The side opposite the 90° angle is the longest side, called the hypotenuse. Therefore the angle opposite the hypotenuse is always 90°.
Question 8: What is the volume of a rectangular box with length 4, width 3, and height 5?
- 12
- 20
- 47
- 60 (Correct answer)
Correct answer: 60
Volume = l × w × h = 4 × 3 × 5 = 60.
The volume of a rectangular prism (box) is V = l × w × h = 4 × 3 × 5 = 60 cubic units.
Bluebook SAT Test Geometry and Trigonometry 1
A right triangle has legs of length 6 and 8.
What is the length of the hypotenuse?