If the side of an equilateral triangle is 'a', what is its altitude?
Answer: C
In an equilateral triangle, the altitude bisects the base. This creates two 30-60-90 right-angled triangles.
The hypotenuse is 'a', the base is 'a/2', and the altitude is 'h'.
Using the Pythagorean theorem: \(h^2 + (a/2)^2 = a^2\)
\(h^2 = a^2 - a^2/4 = \frac{3a^2}{4}\)
\(h = \sqrt{\frac{3a^2}{4}} = \frac{a\sqrt{3}}{2}\).