Question

there is a right triangle with right angle at the top left, vertex labeled c, top right vertex labeled b with a 60° angle, and bottom left vertex labeled a. the side from c to a is labeled b, and the hypotenuse from a to b is labeled 12 units. below the triangle, there are four multiple - choice options: 1. $cos(60^{circ})=\frac{12}{a}$ 2. $cos(60^{circ})=\frac{12}{b}$ 3. $cos(60^{circ})=\frac{b}{a}$ 4. $cos(60^{circ})=\frac{a}{12}$

Explanation:

Step1: Recall the cosine function definition

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify the sides relative to the \(60^{\circ}\) angle

For \(\angle D = 60^{\circ}\) in right - triangle \(ACD\), the adjacent side to \(\angle D\) is \(b\) and the hypotenuse is \(a\).

Answer:

\(\cos(60^{\circ})=\frac{b}{a}\)