Answer:
[tex]sin(G)=0.91[/tex]
Step-by-step explanation:
Recall that [tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex] with respect to the angle [tex]\theta[/tex] for a right triangle. Since we are given our hypotenuse of [tex]\sqrt{85}[/tex] and our adjacent side of [tex]\sqrt{15}[/tex], we can use the Pythagorean Theorem to solve for the missing opposite side:
[tex]a^2+b^2=c^2\\\\(opposite)^2+(adjacent)^2=(hypotenuse)^2\\\\(opposite)^2+(\sqrt{15})^2=(\sqrt{85})^2\\\\(opposite)^2+15=85\\\\(opposite)^2=70\\\\opposite=\sqrt{70}[/tex]
Thus, [tex]sin(G)=\frac{\sqrt{70}}{\sqrt{85}}\approx0.91[/tex]
