Question

Find the missing 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=(15\sqrt2)/(2)\\a\sqrt3=x\\\\a\sqrt3=(15\sqrt2)/(2)\qquad\text{multiply both sides by}\ \sqrt3\\\\3a=(15\sqrt6)/(2)\qquad\text{divide both sides by 3}\\\\a=(5\sqrt6)/(2)\\\\2a=2\cdot(5\sqrt6)/(2)=5\sqrt6`

Answer:

`y=(5\sqrt6)/(2)\\\\x=5\sqrt6`