Question

find tanθ, where θ is the angle shown. give an exact value, not a decimal approximation.

Explanation:

Step1: Recall tangent - ratio formula

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify opposite and adjacent sides

For angle $\theta$, the opposite side has length $\sqrt{9^{2}-8^{2}}=\sqrt{81 - 64}=\sqrt{17}$, and the adjacent side has length 8.

Answer:

$\frac{\sqrt{17}}{8}$