Question

I don't even know how to figure this out. I don't have a formula for this

Answer 1

Answer:

$\sin\theta=\dfrac{15}{17}$

$?=15$

Step-by-step explanation:

Use the trigonometry formula

$\cos^2\theta+\sin^2\theta=1$

You are given that

$\cos \theta=\dfrac{8}{17}$

Substitute into the first formula

$\left(\dfrac{8}{17}\right)^2+\sin^2\theta=1\\ \\\dfrac{64}{289}+\sin^2\theta=1\\ \\\sin^2\theta=1-\dfrac{64}{289}=\dfrac{289-64}{289}=\dfrac{225}{289}\\ \\\sin \theta=\pm \dfrac{15}{17}$

Angle $\theta$ is acute angle, then the sine of this angle is positive and

$\sin\theta=\dfrac{15}{17}$