Question

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

Explanation:

Step1: Identify sides and angles

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

Step2: Substitute values

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

Step3: Find the angle

We know that if $\sin(F)=0.7$, then $F=\sin^{- 1}(0.7)$. Using a calculator, $F\approx44.4^{\circ}$.

Answer:

$44.4^{\circ}$