Question

find the sine of ∠h. simplify your answer and write it as a proper fraction. sin(h) = —

Explanation:

Step1: Find hypotenuse

By Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 8$, $b=15$. So $c=\sqrt{8^{2}+15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17$.

Step2: Use sine - definition

The sine of an angle in a right - triangle is $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle H$, the opposite side to $\angle H$ is $IJ = 15$ and the hypotenuse is $HI=17$. So $\sin(H)=\frac{15}{17}$.

Answer:

$\frac{15}{17}$