Question

express tan s as a fraction in simplest terms.

Explanation:

Step1: Find the length of \( QR \)

Use the Pythagorean theorem \( QR=\sqrt{SQ^{2}-SR^{2}} \). Given \( SQ = 35 \) and \( SR=21 \), then \( QR=\sqrt{35^{2}-21^{2}}=\sqrt{(35 + 21)(35 - 21)}=\sqrt{56\times14}=\sqrt{784}=28 \).

Step2: Calculate \( \tan S \)

By the definition of tangent in a right - triangle \( \tan S=\frac{opposite}{adjacent} \). In right - triangle \( QRS \), for angle \( S \), the opposite side to \( S \) is \( QR = 28 \) and the adjacent side to \( S \) is \( SR=21 \). So \( \tan S=\frac{QR}{SR}=\frac{28}{21}=\frac{4}{3} \).

Answer:

\(\frac{4}{3}\)