Question

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

Explanation:

Step1: Identify sides and angles

In right - triangle FGH, $\angle G = 90^{\circ}$, $GH = 28$, $FH=40$. Let $\angle F$ be the angle we want to find. According to 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 $\sin(F)=\frac{28}{40}\times1=\frac{7}{10}=0.7$.

Step3: Find the angle

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

Answer:

$44.4^{\circ}$