Question

write the equation you would set up for this problem. do not solve. image of a right triangle with one angle 37°, hypotenuse 14, and one leg labeled x

Explanation:

Step1: Identify triangle type

It's a right - triangle with hypotenuse 14, angle 37°, and adjacent side \(x\) to 37°.

Step2: Recall cosine definition

Cosine of an angle in right - triangle is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).
Here, \(\theta = 37^{\circ}\), adjacent \(=x\), hypotenuse \( = 14\). So the equation is \(\cos(37^{\circ})=\frac{x}{14}\) or \(x = 14\cos(37^{\circ})\) (either form is acceptable for setting up).

Answer:

\(\cos(37^{\circ})=\frac{x}{14}\) (or \(x = 14\cos(37^{\circ})\))