Geometry and TrigonometryHardRight triangles and the Pythagorean theorem
Geometry and Trigonometry practice question
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg?
- A. 8
- B. 10
- C. 12Correct
- D. 18
Answer: C. 12
By the Pythagorean theorem, leg² = 13² − 5² = 169 − 25 = 144, so leg = 12. Memorize the 5-12-13 triple to skip the arithmetic on test day.
Why the other answers are wrong
- A. 8
- You subtracted the side lengths directly (13 − 5 = 8); the Pythagorean theorem requires subtracting the squares: 169 − 25 = 144.
- B. 10
- 10 is a plausible-looking length but doesn't come from the theorem — check that 5² + leg² = 13², which forces leg² = 144 and leg = 12.
- D. 18
- You added the two given sides (13 + 5 = 18); the missing leg comes from 13² − 5² = 144, so it's 12.
More Geometry and Trigonometry questions
- Hard
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Hard
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
What is 135° expressed in radians? - Hard
What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector? - Hard
What is the area, in square units, of triangle ABC?
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