Question

Find the missing lengths in the triangle. round to the nearest tenth if necessary

Answer 1

`x=8,\\y\approx 6.9`

Explanation:

The side lengths of all 30-60-90 triangles are in ratio
`x:x√(3):2x}`, where
`2x` is the hypotenuse of the triangle and
`x` is the side opposite to the 30 degree angle.

In the given diagram, the side labelled 4 is opposite to the 30 degree angle. Since
`x` is labelled as the hypotenuse of the triangle,
`x` must be
`4\cdot 2=\boxed{8}`.

Variable
`y` must then represent
`x√(3)` for
`x=4`, yielding
`y=4√(3)\approx \boxed{6.9}`