Question

find the tangent of ∠x. simplify your answer and write it as a proper fraction, improper fraction, or whole number. tan(x) =

Explanation:

Step1: Find side XZ via Pythagoras

$$XZ = \sqrt{XY^2 - YZ^2} = \sqrt{97^2 - 72^2} = \sqrt{9409 - 5184} = \sqrt{4225} = 65$$

Step2: Define tan(∠X) ratio

For $\angle X$, $\tan(X) = \frac{\text{opposite side}}{\text{adjacent side}} = \frac{YZ}{XZ}$

Step3: Substitute values and simplify

$$\tan(X) = \frac{72}{65}$$

Answer:

$\frac{72}{65}$