Question

determining trigonometric ratios of similar triangles consider △abc ~ △xyz what is the value of tan(a)? what is the value of tan(x)? 3/4 3/5 4/5 what is true about the two tangent ratios?

Explanation:

Step1: Recall tangent - ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle A$ in $\triangle ABC$, the side opposite $\angle A$ is $BC = 3$ and the side adjacent to $\angle A$ is $AC = 4$.

Step2: Calculate $\tan(A)$

Using the formula $\tan(A)=\frac{BC}{AC}$, substituting $BC = 3$ and $AC = 4$, we get $\tan(A)=\frac{3}{4}$.
Since $\triangle ABC\sim\triangle XYZ$, corresponding angles are equal, so $\angle A=\angle X$ and $\tan(A)=\tan(X)$.

Answer:

The value of $\tan(A)$ is $\frac{3}{4}$, the value of $\tan(X)$ is $\frac{3}{4}$, and $\tan(A)=\tan(X)$ because corresponding angles of similar triangles are equal and the tangent of equal angles in right - triangles is equal.