Question

Find the missing side lengths of the special right triangle. Leave your answers as radicals in simplest form.

Answer 1

We have been a right triangle. We are asked to find the missing length of the given triangle.

We can see that our given triangle is 30-60-90 triangle.

We know that the lengths of the sides of a 30-60-90 triangle are in the ratio
`1:√(3):2`.

If the side opposite to 30 degree is
`n`, then the side opposite to 60 degree angle will be
`√(3)n` and side opposite to hypotenuse will be
`2n`.

We can see that side corresponding to hypotenuse is 6 that is
`2n=6`.

Let us solve for n.

`(2n)/(2)=(6)/(2)`

`n=3`

The side corresponding to 30 degree angle will be half of 6 that is 3. Therefore, the value of y is 3.

The value of x will be
`3√(3)` as it is side corresponding to 60 degree angle.