Question

For the right triangles below, find the exact values of the side lengths a and h. If necessary, write your responses in simplified radical form. pad 309 8 Х X S 45° 0 60° 3 h

Answer 1

First Triangle:

This is a special right-angled triangle and is known as 45°-45°-90° triangle

To solve for any side length, we can use the following procedure.

As you can see, the sides opposite to the 45° are equal and in this case, both are 3

Then the side opposite 90° will be

`3\sqrt[]{2}`

Therefore, the side a = 3√2

Second Triangle:

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

To solve for any side length, we can use the following procedure.

As you can see, the side opposite the 30° is the smallest.

The side opposite the 60° is 2 times the side 30°

The side opposite the 90° is √3 times the side 30°

For the given case, we want to know the side opposite of side 30°

We are given the side opposite the 60° that is 8

`\begin{gathered} 2h=8 \\ h=(8)/(2) \\ h=4 \end{gathered}`

Therefore, side h = 4