Question

find x. round your answer to the nearest integer. right triangle with right angle, hypotenuse 10, angle 37° at the base vertex, base length x. options: a. 5, b. 6, c. 7, d. 8

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, $\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 37^\circ$, adjacent side is $x$, hypotenuse is $10$. So $\cos(37^\circ) = \frac{x}{10}$.

Step2: Solve for x

Multiply both sides by 10: $x = 10 \times \cos(37^\circ)$. Using a calculator, $\cos(37^\circ) \approx 0.8$, so $x \approx 10 \times 0.8 = 8$ (rounded to nearest integer).

Answer:

D. 8