Question

if tan θ = 2/7 and the measure of (overline{xy}) is 2 units, what is the measure of (overline{yz})?

Explanation:

Step1: Recall tangent formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let $\theta$ be the angle at vertex $X$, the opposite side to $\theta$ is $\overline{YZ}$ and the adjacent side is $\overline{XZ}$. Given $\tan\theta = \frac{2}{7}$ and assume the length of $\overline{YZ}=2x$ and the length of $\overline{XZ} = 7x$.

Step2: Use given side - length information

If we assume the side - length relationship based on the tangent ratio, and we know that if the side corresponding to the numerator of the tangent ratio (opposite side) has a length of 2 units (assuming $x = 1$), then the side corresponding to the denominator of the tangent ratio (adjacent side) has a length of 7 units.

Answer:

7 units