Question

How do you find the remaining side of a `30^circ-60^circ-90^circ` triangle if the longest side is 8?

Answer 1

The three sides are 4, `4sqrt(3)`, and 8.

Explanation:

The ratio of the sides in a 30-60-90 triangle is `x:xsqrt(3):2x`. That means if the side opposite `30^circ` is `x`, then the side opposite `60^circ` is `xsqrt(3)` and the side opposite `90^circ` is `2x`.

Since the longest side is the hypotenuse, which is opposite `90^circ`, we know that `2x = 8\rightarrow x = 4`. So the side opposite `30^circ` is 4.

If the side opposite `30^circ` is 4, we know that the side opposite `60^circ`, `xsqrt(3)`, is going to be `4sqrt(3)`.

So the sides are 4, `4sqrt(3)`, and 8.