Question

use the triangle shown to the right to evaluate the following expression. if necessary, express the value without a square root in the denominator by rationalizing the denominator. cos 30°

Explanation:

Step1: Recall cosine definition

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify sides for 30 - degree angle

For the $30^{\circ}$ angle in the given right - triangle, the adjacent side to the $30^{\circ}$ angle is $\sqrt{3}$ and the hypotenuse is 2.
So, $\cos30^{\circ}=\frac{\sqrt{3}}{2}$.

Answer:

$\frac{\sqrt{3}}{2}$