Question

Find the values of x and y. Round your answers to the nearest tenth if necessary,

Answer 1

`\huge\boxed{x=12;\ y=12\sqrt3\approx20.8}`

Explanation:

Look at the picture.

We have:

`2a=24\\a=x\\a\sqrt3=y`

Therefore:

`x=24:2=12\\\\y=12\sqrt3\approx12\cdot1.73=20.76\approx20.8`

Answer 2

`x=12,\\y=12√(3)`

Explanation:

In any 30-60-90 triangle, the side lengths are in the ratio
`x:x√(3):2x`, where
`2x` is the hypotenuse, or longest side, of the triangle and
`x` is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since
`x` is opposite to the 30 degree angle,

Therefore, we have:

`x=(24)/(2),\\x=\boxed{12}`

Based on our side length ratio
`x:x√(3):2x`,
`y` is then:

`y=x√(3)\text{ for}\implies x=12,\\y=\boxed{12√(3)}`