SAT Math
Right Triangles and Trigonometry
Right Triangles and Trigonometry is a skill in the Geometry and Trigonometry domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
12 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
The legs of a right triangle measure 5 and 12. What is the length of the hypotenuse?
- A. 7
- B. 13 ✓
- C. 8.5
- D. 17
Correct answer: B. By the Pythagorean theorem, the hypotenuse is √(5² + 12²) = √(25 + 144) = √169 = 13.
In a 30-60-90 triangle, the hypotenuse measures 14. What is the length of the side opposite the 60° angle?
- A. 7√2
- B. 7
- C. 7√3 ✓
- D. 14√3
Correct answer: C. In a 30-60-90 triangle, the side opposite 60° equals half the hypotenuse times √3; half of 14 is 7, so the side is 7√3.
In right triangle ABC, angle C is the right angle. If sin(A) = 0.6, what is the value of cos(B)?
- A. 0.4
- B. 0.8
- C. −0.6
- D. 0.6 ✓
Correct answer: D. Angles A and B are complementary (they sum to 90°) in a right triangle, and sine and cosine of complementary angles are always equal, so cos(B) = sin(A) = 0.6.
An equilateral triangle has an altitude of length 9 times the square root of 3. What is the perimeter of the triangle?
- A. 54 ✓
- B. 27
- C. 36
- D. 81
Correct answer: A. Correct — the altitude of an equilateral triangle with side s satisfies altitude = (s times the square root of 3) / 2; setting that equal to 9 times the square root of 3 gives s = 18, so the perimeter is 3 times 18, or 54.
In a right triangle, sin(theta) = 5/13. What is the value of cos(theta) times tan(theta)?
- A. 12/13
- B. 5/13 ✓
- C. 5/12
- D. 60/169
Correct answer: B. Correct — using the 5-12-13 triangle, cos(theta) = 12/13 and tan(theta) = 5/12, so cos(theta) times tan(theta) = (12/13)(5/12) = 5/13, which is simply sin(theta) itself, since cos(theta) times tan(theta) always equals sin(theta).