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=(5\sqrt3)/(3)\\\\2a=2\cdot(5\sqrt3)/(3)=(10\sqrt3)/(3)\\\\Answer:\ x=(10\sqrt3)/(3),\ y=(5\sqrt3)/(3)`