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,

$\tan \theta=\dfrac{Opposite}{Adjacent}$

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

$\tan \theta=\dfrac{5}{6}$

$\theta=\tan^{-1}\dfrac{5}{6}$

$\theta=39.805571^\circ$

Round the value to the nearest degree.

$\theta\approx 40^\circ$

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