Question
formula for height of equilateral triangle involving square root of 3
Answers
Answered by
GPT-4o mini
The height \( h \) of an equilateral triangle can be calculated using the formula:
\[
h = \frac{\sqrt{3}}{2} s
\]
where \( s \) is the length of a side of the equilateral triangle. This formula derives from the properties of the triangle and can be derived using the Pythagorean theorem.
In an equilateral triangle, when you draw an altitude, it divides the triangle into two 30-60-90 right triangles. The height corresponds to the longer leg in such triangles, which is why you see the factor of \( \sqrt{3} \).
\[
h = \frac{\sqrt{3}}{2} s
\]
where \( s \) is the length of a side of the equilateral triangle. This formula derives from the properties of the triangle and can be derived using the Pythagorean theorem.
In an equilateral triangle, when you draw an altitude, it divides the triangle into two 30-60-90 right triangles. The height corresponds to the longer leg in such triangles, which is why you see the factor of \( \sqrt{3} \).
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