Question

Find the missing side lengths. Leave your answers as radicals in simplest form

Answer 1

We have the triangle 30° - 60° - 90°.

The lenght of the sides are in proportion: $1:2:\sqrt3\to a:2a:a\sqrt3$

$a=y\\2a=x\\a\sqrt3=5\\\\a\sqrt3=5\qquad\text{multiply both sides by}\ \sqrt3\\\\3a=5\sqrt3\qquad\text{divide both sides by 3}\\\\a=\dfrac{5\sqrt3}{3}\\\\2a=2\cdot\dfrac{5\sqrt3}{3}=\dfrac{10\sqrt3}{3}\\\\Answer:\ x=\dfrac{10\sqrt3}{3},\ y=\dfrac{5\sqrt3}{3}$