what is the approximate measure of angle f? use the law of sines to find the answer. law of sines…

Explanation:

Step1: Identify sides and angles

In right - triangle FGH, assume angle G = 90°, side GH = 28, and side FH = 40. We want to find angle F. By the law of sines, $\frac{\sin(F)}{GH}=\frac{\sin(G)}{FH}$.

Step2: Substitute values

Since $\sin(G)=\sin(90^{\circ}) = 1$, we have $\sin(F)=\frac{GH}{FH}\times\sin(G)$. Substituting GH = 28, FH = 40, and $\sin(G)=1$ into the formula, we get $\sin(F)=\frac{28}{40}\times1=\frac{28}{40}=0.7$.

Step3: Find the angle

To find angle F, we take the inverse - sine of 0.7. So, $F=\sin^{- 1}(0.7)\approx44.4^{\circ}$.

Answer:

44.4°