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? 13.1 inches 7.7 inches 8.4 inches 6.4 inches

Explanation:

Step1: Identify the cosine formula

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 40^{\circ}$ and the hypotenuse $c = 10$ inches. Let the side adjacent to angle $C$ be $a$. So, $\cos C=\frac{a}{c}$.

Step2: Substitute the values

We know that $\cos40^{\circ}\approx0.766$ and $c = 10$. Substituting into the formula $a = c\times\cos C$, we get $a=10\times\cos40^{\circ}$.

Step3: Calculate the value of $a$

$a = 10\times0.766=7.66\approx7.7$ inches.

Answer:

7.7 inches