Question

what is the approximate measure of angle f? use the law of sines to find the answer. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$ 11.5° 44.4° 68.0° 81.9°

Explanation:

Step1: Identify sides and angles

In right - triangle FGH, side GH = 28, side FH = 40, and angle G = 90°. We want to find angle F. According to the law of sines $\frac{\sin(F)}{GH}=\frac{\sin(H)}{FH}=\frac{\sin(G)}{FG}$. Since $\sin(G)=\sin(90^{\circ}) = 1$, and we know GH and FH.

Step2: Apply the law of sines

We have $\frac{\sin(F)}{28}=\frac{\sin(90^{\circ})}{40}$. Since $\sin(90^{\circ}) = 1$, the equation becomes $\sin(F)=\frac{28}{40}=0.7$.

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°