Question

let $\theta$ equal the acute angle the wire makes with the ground. which ratio describes $\tan\theta$? a. $\frac{h}{w}$ b. $\frac{g}{w}$ c. $\frac{h}{g}$ d. $\frac{g}{h}$

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, the tangent of an acute angle $\theta$ is defined as the ratio of the length of the opposite side to the length of the adjacent side.

Step2: Identify opposite and adjacent sides

For the angle $\theta$ (the angle the wire makes with the ground), the opposite side is the height $h$ of the point where the wire is attached to the tree and the adjacent side is the distance $g$ from the base of the tree to the point where the wire is anchored on the ground. So, $\tan\theta=\frac{h}{g}$.

Answer:

C. $\frac{h}{g}$