Question

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

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 8\) and \(b=15\). So \(c=\sqrt{8^{2}+ 15^{2}}=\sqrt{64 + 225}=\sqrt{289}=17\).

Step2: Recall sine - definition

The sine of an angle in a right - triangle is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). 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:

\(\frac{15}{17}\)