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

Help in 13.Use special right triangles to help you find the missing sides-example-1

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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

Help in 13.Use special right triangles to help you find the missing sides-example-1
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