Geometry and TrigonometryHardAltitude to the hypotenuse
Geometry and Trigonometry practice question
A right triangle has legs of length 5 and 12 and a hypotenuse of length 13. What is the length of the altitude drawn from the right angle to the hypotenuse? Give the answer as a fraction.
Answer: 60/13
Area = (1/2)(5)(12) = 30, and also (1/2)(13)h, so h = 60/13.
Common wrong answers
- If you answered 6
- 6 is not the altitude for this triangle; the area route gives 60/13.
- If you answered 12
- 12 is a leg, not the altitude to the hypotenuse.
- If you answered 30/13
- 30/13 uses the area 30 without doubling it.
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