SAT · Additional Topics in Math · Right triangle trigonometry
Question sat-q-00177
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The question
In a right triangle, the two legs have lengths 5 and 12. What is the length of the hypotenuse?
- 14
- 17
- 13
- 12
Show answer & worked solution
Answer: 13
Worked solution. By the Pythagorean theorem, hypotenuse = √(5² + 12²) = √(169) = 13. (You may also recognize this as a Pythagorean triple.)
Why each wrong choice is wrong. The trap distractor adds the legs instead of using the Pythagorean theorem. Off-by-one distractors catch arithmetic slips.
Test-day tactic. Memorize the common Pythagorean triples. When you see one, you save the time of squaring and square-rooting.
About this question type
Items test the basic trig ratios (sine, cosine, tangent), the special right triangles (30-60-90 and 45-45-90), and the Pythagorean theorem. Common surface forms include finding a missing side given an angle and a side, finding an angle given two sides, or recognizing a Pythagorean triple in disguise.
You will see a question shaped like this one on roughly every other official SAT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.