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 known values

In right triangle $FGH$: $\angle G = 90^\circ$, side opposite $\angle F$ is $GH = 28$, side opposite $\angle G$ is $FH = 40$.

Step2: Apply Law of Sines

Set up ratio for $\angle F$ and $\angle G$:
$$\frac{\sin(F)}{GH} = \frac{\sin(G)}{FH}$$
Substitute values:
$$\frac{\sin(F)}{28} = \frac{\sin(90^\circ)}{40}$$
Since $\sin(90^\circ)=1$:
$$\sin(F) = \frac{28}{40} = 0.7$$

Step3: Calculate $\angle F$

Use inverse sine function:
$$\angle F = \arcsin(0.7)$$
Calculate approximate value:
$$\angle F \approx 44.4^\circ$$

Answer:

44.4°