In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.
cos 30°

Key Concepts

Trigonometric Ratios

Trigonometric ratios are relationships between the angles and sides of a right triangle. The primary ratios include sine, cosine, and tangent, defined as the ratios of the lengths of the sides opposite, adjacent, and hypotenuse to a given angle. For example, in triangle PQR, cos(30°) is calculated as the length of the adjacent side (QR) over the hypotenuse (PR).

Special Right Triangles

Special right triangles, specifically the 30-60-90 triangle, have known side ratios that simplify calculations. In a 30-60-90 triangle, the sides opposite the 30°, 60°, and 90° angles are in the ratio 1:√3:2. This means that if the shortest side is 1, the longer leg is √3, and the hypotenuse is 2, making it easier to find trigonometric values without complex calculations.

Rationalizing the Denominator

Rationalizing the denominator is a process used to eliminate square roots or irrational numbers from the denominator of a fraction. This is often done by multiplying the numerator and denominator by a suitable value that will result in a rational number in the denominator. For example, if the expression involves a square root in the denominator, multiplying by that square root can help simplify the expression.