Question

in a right triangle, angle c measures 40°. the hypotenuse of the triangle is 10 inches long. what is the approximate length of the side adjacent to angle c?
6.4 inches
7.7 inches
8.4 inches
13.1 inches

Explanation:

Step1: Recall cosine definition

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 40^\circ$, hypotenuse = 10 inches.

Step2: Solve for adjacent side

Let adjacent side be $x$. So $\cos(40^\circ) = \frac{x}{10}$. Then $x = 10 \times \cos(40^\circ)$. Calculate $\cos(40^\circ) \approx 0.7660$, so $x \approx 10 \times 0.7660 = 7.66 \approx 7.7$ inches.

Answer:

7.7 inches (corresponding to the option with 7.7 inches)