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

Triangle FGH right-angled at G; GH=28, FH=40 (hypotenuse); angle F opposite GH.

Step2: Apply Law of Sines

$\frac{\sin(F)}{GH} = \frac{\sin(G)}{FH}$; $\sin(G)=1$ (90°), so $\sin(F)=\frac{28}{40}=0.7$.

Step3: Calculate angle F

$F=\arcsin(0.7)\approx44.4^\circ$.

Answer:

B. 44.4°