Question

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

Explanation:

Step1: Identify known sides in $\triangle XYZ$

In right $\triangle XYZ$, hypotenuse $ZY=26$, adjacent side to $\angle Z$: $XZ=10$

Step2: Calculate opposite side $XY$

Use Pythagorean theorem: $XY=\sqrt{ZY^2 - XZ^2}=\sqrt{26^2 - 10^2}=\sqrt{676-100}=\sqrt{576}=24$

Step3: Apply tangent definition for $\angle Z$

$\tan(Z)=\frac{\text{opposite}}{\text{adjacent}}=\frac{XY}{XZ}$
$\tan(Z)=\frac{24}{10}=\frac{12}{5}$

Answer:

$\frac{12}{5}$