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^{\circ}\\) \\(\cos 30^{\circ} = \square\\) (type an exact answer, using radicals as needed. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Recall cosine definition

For an acute angle in a right triangle, $\cos\theta = \frac{\text{adjacent side}}{\text{hypotenuse}}$

Step2: Identify sides for $30^\circ$

Adjacent side to $30^\circ$ is $\sqrt{3}$, hypotenuse is $2$.

Step3: Substitute into formula

$\cos 30^\circ = \frac{\sqrt{3}}{2}$

Answer:

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