Question

the picture below shows a right - triangle - shaped charging stand for a gaming system. which expression shows the length of side ab? 8(cos 60°) $\frac{8}{sin 60^{circ}}$ $\frac{8}{cos 60^{circ}}$ 8(tan 60°)

Explanation:

Step1: Recall cosine - ratio in right - triangle

In right - triangle $\triangle ABC$ with right - angle at $C$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 60^{\circ}$, the adjacent side to $\angle B$ is $BC = 8$ inches and the hypotenuse is $AB$. So, $\cos60^{\circ}=\frac{BC}{AB}$.

Step2: Solve for $AB$

From $\cos60^{\circ}=\frac{BC}{AB}$, we can cross - multiply to get $AB\times\cos60^{\circ}=BC$. Then, $AB=\frac{BC}{\cos60^{\circ}}$. Since $BC = 8$ inches, $AB=\frac{8}{\cos60^{\circ}}$.

Answer:

$\frac{8}{\cos60^{\circ}}$