Question

Find the measure of the indicated angle to the nearest degree.

Answer 1

Given:

A right triangle with legs 5 units and 6 units.

To find:

The measure of angle opposite of side whose length is 5 units.

Solution:

In a right angle triangle,

`\tan \theta=(Opposite)/(Adjacent)`

Let
`\theta` be the missing angle. Then, for the given triangle,

`\tan \theta=(5)/(6)`

`\theta=\tan^(-1)(5)/(6)`

`\theta=39.805571^\circ`

Round the value to the nearest degree.

`\theta\approx 40^\circ`

Therefore, the measure of the required angle is 40 degrees.