Question

Help in 13.Use special right triangles to help you find the missing sides

Answer 1

We are asked to find the missing sides of the given right-angled triangle.

This is a special right-angled triangle known as the "30°-60°-90°" triangle.

There is a fixed ratio of side lengths in such a triangle.

As you can see, the lengths of sides are

Side opposite of 30° = x

Side opposite of 60° = x√3

Side opposite of 90° = 2x

We are given the side opposite to 60°

So, we can write

`\begin{gathered} x\sqrt[]{3}=11\sqrt[]{3} \\ x=\frac{11\sqrt[]{3}}{\sqrt[]{3}} \\ x=11 \end{gathered}`

So, the length of the side opposite of 30° is 11

And the length of the side opposite of 90° is

`2x=2(11)=22`

Therefore, the side lengths of the given triangle are

Side opposite of 30° = x = 11

Side opposite of 60° = x√3 = 11√3

Side opposite of 90° = 2x = 22