Question

In ΔFGH, the measure of ∠H=90°, GF = 53, HG = 28, and FH = 45. What ratio represents the sine of ∠G?

Answer 1

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.

$\text{sin}=\frac{\text{Opposite}}{\text{hypotenuse}}$

We can see from the attachment that opposite side to angle G is FH and hypotenuse is GF.

$\text{sin}(\angle G)=\frac{FH}{GF}$

$\text{sin}(\angle G)=\frac{45}{53}$

Therefore, the ratio $\frac{45}{53}$ represents the sine of ∠G.