Question

which equation can be used to find the length of side x?
a. $x = 32sin25^{circ}$
b. $x = 32cos25^{circ}$
c. $x=\frac{32}{cos25^{circ}}$
d. $x=\frac{32}{sin25^{circ}}$

Explanation:

Step1: Recall sine - cosine - tangent relations

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, the angle is $25^{\circ}$, the hypotenuse is 32, and the side $x$ is adjacent to the $25^{\circ}$ angle.

Step2: Apply cosine formula

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Substituting $\theta = 25^{\circ}$, adjacent side $=x$ and hypotenuse $ = 32$, we get $\cos25^{\circ}=\frac{x}{32}$.

Step3: Solve for $x$

Cross - multiply the equation $\cos25^{\circ}=\frac{x}{32}$ to get $x = 32\cos25^{\circ}$.

Answer:

B. $x = 32\cos25^{\circ}$