Question

1. find sin r, cos r, tan r, sin s, cos s, and tan s. express each ratio as a fraction and as a decimal to the nearest hundredth.

Explanation:

Step1: Confirm right triangle sides

For right $\triangle RTS$ (right angle at $T$):

• Hypotenuse $RS = 34$
• Leg $RT = 30$, Leg $ST = 16$

Step2: Calculate ratios for $\angle R$

$\sin R$: Opposite/Hypotenuse

$\sin R = \frac{ST}{RS} = \frac{16}{34} = \frac{8}{17} \approx 0.47$

$\cos R$: Adjacent/Hypotenuse

$\cos R = \frac{RT}{RS} = \frac{30}{34} = \frac{15}{17} \approx 0.88$

$\tan R$: Opposite/Adjacent

$\tan R = \frac{ST}{RT} = \frac{16}{30} = \frac{8}{15} \approx 0.53$

Step3: Calculate ratios for $\angle S$

$\sin S$: Opposite/Hypotenuse

$\sin S = \frac{RT}{RS} = \frac{30}{34} = \frac{15}{17} \approx 0.88$

$\cos S$: Adjacent/Hypotenuse

$\cos S = \frac{ST}{RS} = \frac{16}{34} = \frac{8}{17} \approx 0.47$

$\tan S$: Opposite/Adjacent

$\tan S = \frac{RT}{ST} = \frac{30}{16} = \frac{15}{8} = 1.88$

Answer:

• $\sin R = \frac{8}{17} \approx 0.47$
• $\cos R = \frac{15}{17} \approx 0.88$
• $\tan R = \frac{8}{15} \approx 0.53$
• $\sin S = \frac{15}{17} \approx 0.88$
• $\cos S = \frac{8}{17} \approx 0.47$
• $\tan S = \frac{15}{8} = 1.88$