Question

rs = 504, st = 128, tr = 520. 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 65/16 b 63/16 c 65/63 d 16/63

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Since $\triangle RST\sim\triangle UVW$ and $\angle T$ corresponds to $\angle W$, $\tan W=\tan T$.

Step2: Identify opposite and adjacent sides for $\angle T$ in $\triangle RST$

In right - triangle $RST$, for $\angle T$, the opposite side is $RS = 504$ and the adjacent side is $ST=128$.

Step3: Calculate $\tan T$ (which is equal to $\tan W$)

$\tan T=\frac{RS}{ST}=\frac{504}{128}=\frac{63}{16}$.

Answer:

B. $\frac{63}{16}$