Question

find the sine of ∠u. write your answer in simplified, rationalized form. do not round. sin(u) =

Explanation:

Step1: Recall sine - ratio definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle U$, the side opposite to $\angle U$ is $VT = 2$, and the hypotenuse is $UV=\sqrt{13}$.

Step2: Calculate sine value

$\sin(U)=\frac{2}{\sqrt{13}}$.

Step3: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{13}$: $\frac{2\times\sqrt{13}}{\sqrt{13}\times\sqrt{13}}=\frac{2\sqrt{13}}{13}$.

Answer:

$\frac{2\sqrt{13}}{13}$