find the tangent of ∠s. simplify your answer and write it as a proper fraction, improper fraction, or whole…

Answer:

$\frac{15}{8}$

Explanation:

Step1: Find side QR using Pythagorean theorem

Let $QR = x$. By $a^{2}+b^{2}=c^{2}$, we have $x^{2}+16^{2}=34^{2}$. So $x^{2}=34^{2}-16^{2}=(34 + 16)(34 - 16)=50\times18 = 900$, then $x = 30$.

Step2: Calculate tangent of ∠S

The tangent of an angle in a right - triangle is the ratio of the opposite side to the adjacent side. For $\angle S$, the opposite side to $\angle S$ is $QR = 30$ and the adjacent side is $RS=16$. So $\tan(S)=\frac{30}{16}=\frac{15}{8}$.