Question

use the diagram and side lengths of triangle rst to determine the angles used for the trigonometric ratios. sin(< ) = 12/13, tan(< ) = 5/12

Explanation:

Step1: Recall trig - ratio definitions

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify sides for $\sin$

For $\sin(\theta)=\frac{12}{13}$, in right - triangle RST, if we consider angle $T$, opposite side to $T$ is 24 and hypotenuse is 26. Reducing $\frac{24}{26}=\frac{12}{13}$, so $\sin(T)=\frac{12}{13}$.

Step3: Identify sides for $\tan$

For $\tan(\theta)=\frac{5}{12}$, if we consider angle $R$, opposite side to $R$ is 10 and adjacent side is 24. Reducing $\frac{10}{24}=\frac{5}{12}$, so $\tan(R)=\frac{5}{12}$.

Answer:

$\sin(T)=\frac{12}{13}$, $\tan(R)=\frac{5}{12}$