Question

find: \sin v

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for $\angle V$

For $\angle V$, opposite side to $V$ is $TU$, hypotenuse is $TV = 26$. First, find $TU$ using Pythagoras: $TU=\sqrt{TV^2 - VU^2}=\sqrt{26^2 - 10^2}=\sqrt{676 - 100}=\sqrt{576}=24$.

Step3: Calculate $\sin V$

$\sin V=\frac{TU}{TV}=\frac{24}{26}=\frac{12}{13}$.

Answer:

$\frac{12}{13}$