Geometry and TrigonometryMediumPerimeter of a 30-60-90 triangle from its hypotenuse
Geometry and Trigonometry practice question
A right triangle has a hypotenuse of length 10 and one acute angle of 30°. What is the perimeter of the triangle? Round to the nearest tenth.
Answer: 23.7
The side opposite 30° is 10 sin 30° = 5; the other leg is 10 cos 30° = 5√3 ≈ 8.66. Perimeter: 10 + 5 + 8.66 ≈ 23.7.
Common wrong answers
- If you answered 15
- 15 adds the hypotenuse and the short leg only.
- If you answered 20
- 20 doubles the hypotenuse.
- If you answered 13.7
- 13.7 adds the two legs but forgets the hypotenuse.
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