we have been given that in ΔFGH, the measure of ∠H=90°, GF = 53, HG = 28, and FH = 45. We are asked to find the ratio that represents the sine of ∠G.
First of all, we will draw a right triangle using our given information.
We know that sine relates opposite side of right triangle with hypotenuse.
[tex]\text{sin}=\frac{\text{Opposite}}{\text{hypotenuse}}[/tex]
We can see from the attachment that opposite side to angle G is FH and hypotenuse is GF.
[tex]\text{sin}(\angle G)=\frac{FH}{GF}[/tex]
[tex]\text{sin}(\angle G)=\frac{45}{53}[/tex]
Therefore, the ratio [tex]\frac{45}{53}[/tex] represents the sine of ∠G.
