Answer:
[tex]\sin\theta=\dfrac{15}{17}[/tex]
[tex]?=15[/tex]
Step-by-step explanation:
Use the trigonometry formula
[tex]\cos^2\theta+\sin^2\theta=1[/tex]
You are given that
[tex]\cos \theta=\dfrac{8}{17}[/tex]
Substitute into the first formula
[tex]\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}[/tex]
Angle [tex]\theta[/tex] is acute angle, then the sine of this angle is positive and
[tex]\sin\theta=\dfrac{15}{17}[/tex]
