Question

Find the missing side Lengths (70 POINTS!)

Answer 1

x=18

y=
`\sqrt 18`

Explanation:

Answer 2

The sides are as follows:
`x=18,\,\,\,y=9√(3)`

Explanation:

Starting with the side y, we can use the tan to solve for y:

`\tan 30^\circ = (9)/(y)\implies y = (9)/(\tan 30^\circ)={9}√(3)`

The side x can be determined using sin:

`\sin 30^\circ = (9)/(x)\implies x = (9)/(\sin 30^\circ)= 18`

So, the sides as as follows:
`x=18,\,\,\,y=9√(3)`

(you can also verify this result is correct using the Pythagorean theorem)