Question

the side - lengths of right triangle rst are given. triangle rst is similar to triangle uvw, where s corresponds to v and t corresponds to w. what is the value of tan w? a. $\frac{20}{101}$ b. $\frac{20}{99}$ c. $\frac{101}{99}$ d. $\frac{99}{20}$ rs = 792, st = 160, tr = 808

Explanation:

Step1: Recall tangent formula for right - triangles

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For similar right - triangles, the ratios of corresponding sides are equal.

Step2: Identify corresponding sides

Since $\triangle RST\sim\triangle UVW$, and we want to find $\tan W$. In $\triangle RST$, if we consider the angle corresponding to $W$ (say $\angle T$), $\tan T=\frac{RS}{ST}$.

Step3: Calculate the value of the tangent

Given $RS = 792$ and $ST=160$, then $\tan T=\frac{792}{160}=\frac{99}{20}$. Since $\triangle RST\sim\triangle UVW$, $\tan W=\tan T=\frac{99}{20}$.

Answer:

b. $\frac{99}{20}$