Question

express $\sin \theta$ as a fraction in simplest terms.
answer
$\sin \theta =$

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(c = \sqrt{a^{2}+b^{2}}\), where \(a = 4\) and \(b = 8\).
\(c=\sqrt{4^{2}+8^{2}}=\sqrt{16 + 64}=\sqrt{80}=4\sqrt{5}\)

Step2: Use the sine formula

The sine of an angle in a right - triangle is \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For angle \(I\), the opposite side to angle \(I\) is \(4\).
\(\sin I=\frac{4}{4\sqrt{5}}=\frac{1}{\sqrt{5}}=\frac{\sqrt{5}}{5}\)

Answer:

\(\frac{\sqrt{5}}{5}\)