Question

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

Explanation:

Step1: Recall sine - ratio definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle H$, the side opposite to $\angle H$ is $GF = 5$, and the hypotenuse is $GH=\sqrt{82}$.

Step2: Write the sine value

$\sin(H)=\frac{5}{\sqrt{82}}$.

Step3: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{82}$: $\sin(H)=\frac{5\sqrt{82}}{82}$.

Answer:

$\frac{5\sqrt{82}}{82}$