Geometry and TrigonometryVery hardArea of a right triangle from its hypotenuse and an angle
Geometry and Trigonometry practice question
A right triangle has a hypotenuse of length 10 and one acute angle measuring 60°. What is the area of the triangle?
- A. 25√3/2Correct
- B. 25√3
- C. 25/2
- D. 50√3
Answer: A. 25√3/2
This is a 30°-60°-90° triangle: the short leg is half the hypotenuse, 5, and the long leg is 5√3. Area = (1/2)(5)(5√3) = 25√3/2.
Why the other answers are wrong
- B. 25√3
- 25√3 is the product of the legs without the 1/2.
- C. 25/2
- 25/2 uses 5 for both legs, as if the triangle were isosceles; the second leg is 5√3.
- D. 50√3
- 50√3 is 10 × 5√3, using the hypotenuse as a leg.
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