Geometry and TrigonometryMediumLonger leg from the hypotenuse of a 30-60-90 triangle
Geometry and Trigonometry practice question
The hypotenuse of a 30°-60°-90° right triangle has length 10. What is the length of the longer leg?
- A. 5√3Correct
- B. 5
- C. 10√3
- D. 5√2
Answer: A. 5√3
In a 30°-60°-90° triangle the sides are in the ratio 1 : √3 : 2. The hypotenuse is 10, so the short leg is 5 and the longer leg is 5√3.
Why the other answers are wrong
- B. 5
- 5 is the SHORTER leg (half the hypotenuse). The longer leg is √3 times that.
- C. 10√3
- 10√3 multiplies the hypotenuse by √3. The longer leg is √3 times the SHORT leg, 5.
- D. 5√2
- 5√2 belongs to a 45°-45°-90° triangle. Here the ratio involves √3.
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