Question

1. given right triangle \\( \triangle pqr \\) where \\( \angle r \\) is the right angle. if \\( \tan q = \frac { 8 } { 15 } \\) and \\( \cos q = \frac { 15 } { 17 } \\), what is \\( \sin q \\)? show your work #4 by drawing the triangle 15 \\( \frac { 17 } { 15 } \\) 8 \\( \frac { 8 } { 17 } \\)

Explanation:

Step1: Recall the trigonometric identity

We know the identity \(\tan\theta=\frac{\sin\theta}{\cos\theta}\).

Step2: Substitute the given values

Given \(\tan Q = \frac{8}{15}\) and \(\cos Q=\frac{15}{17}\). Substituting into \(\tan Q=\frac{\sin Q}{\cos Q}\), we get \(\frac{8}{15}=\frac{\sin Q}{\frac{15}{17}}\).

Step3: Solve for \(\sin Q\)

Cross - multiply: \(\sin Q=\frac{8}{15}\times\frac{15}{17}\). The \(15\) in the numerator and denominator cancels out.

Answer:

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