Question

1. which of the following equations matches the diagram?

a. $x = \frac{25}{\cos 40^\circ}$
b. $\cos 40^\circ = \frac{x}{25}$
c. $x = \frac{25}{\sin 40^\circ}$
d. $\sin 40^\circ = \frac{25}{x}$

1. find the value of $x$. round to the nearest tent.

(diagram: a right triangle with one angle 40°, one leg 25, hypotenuse x)

Explanation:

Step1: Identify trigonometric ratio

For the $40^\circ$ angle, the adjacent side is 25, and the hypotenuse is $x$. The cosine function relates adjacent and hypotenuse:
$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$
Substitute values: $\cos(40^\circ) = \frac{25}{x}$
Rearrange to solve for $x$: $x = \frac{25}{\cos(40^\circ)}$
This matches option I.

Step2: Calculate value of $x$

First, find $\cos(40^\circ) \approx 0.7660$
Substitute into the formula:
$x = \frac{25}{0.7660} \approx 32.6$

Answer:

a. I. $x = \frac{25}{\cos 40}$
b. 32.6