Geometry and TrigonometryHardHeight of an equilateral triangle
Geometry and Trigonometry practice question
An equilateral triangle has sides of length 8. What is the height of the triangle?
- A. 4√3Correct
- B. 8√3
- C. 4
- D. 4√2
Answer: A. 4√3
The height splits the triangle into two 30°-60°-90° triangles with hypotenuse 8 and short leg 4. The height is the long leg: 4√3.
Why the other answers are wrong
- B. 8√3
- 8√3 is twice the height; the long leg is √3 times the SHORT leg, which is 4.
- C. 4
- 4 is the short leg (half the base), not the height.
- D. 4√2
- 4√2 belongs to a 45°-45°-90° triangle; an equilateral triangle's height involves √3.
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