Question

if \\( \tan \theta = \frac { 8 } { 15 } \\), what is \\( \sin \theta \\)? \\( \sin \theta = \frac {? } { \square } \\)

Explanation:

Step1: Find the hypotenuse

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

Step2: Calculate \(\sin\theta\)

\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), the opposite side to \(\theta\) is \(8\) and hypotenuse is \(17\).
\(\sin\theta=\frac{8}{17}\)

Answer:

\(\frac{8}{17}\)