Question

consider △abc - △xyz. what is the value of tan(a)? what is the value of tan(x)? what is true about the two tangent ratios?

Explanation:

Step1: Recall tangent formula

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$

Step2: Calculate $\tan(A)$

In $\triangle ABC$, $\tan(A)=\frac{3}{4}$

Step3: Calculate $\tan(X)$

In $\triangle XYZ$, $\tan(X)=\frac{6}{8}=\frac{3}{4}$

Step4: State relationship

The two tangent - ratios are equal.

Answer:

$\tan(A)=\frac{3}{4}$, $\tan(X)=\frac{3}{4}$, the two tangent ratios are equal.