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 triangle elements

Right angle at G, GH=28, FH=40 (hypotenuse).

Step2: Apply Law of Sines

$\frac{\sin(F)}{GH} = \frac{\sin(G)}{FH}$

Step3: Substitute values

$\sin(F) = \frac{GH \cdot \sin(G)}{FH} = \frac{28 \cdot 1}{40} = 0.7$

Step4: Calculate angle F

$F = \arcsin(0.7) \approx 44.4^\circ$

Answer:

B. 44.4°