Question

g 28 h
f
40
law of sines: \\(\frac{\sin(a)}{a} = \frac{\sin(b)}{b} = \frac{\sin(c)}{c}\\)
what is the approximate measure of angle f? use the law of sines to find the answer.
\\(11.5^\circ\\)
\\(44.4^\circ\\)
\\(68.0^\circ\\)
\\(81.9^\circ\\)

Explanation:

Step1: Apply the law of sines

In \(\triangle FGH\), \(\angle G = 90^{\circ}\), \(GH = 28\), \(FH = 40\). By the law of sines \(\frac{\sin F}{GH}=\frac{\sin G}{FH}\).

Step2: Substitute the values

Since \(\sin G=\sin90^{\circ} = 1\), we have \(\sin F=\frac{GH}{FH}\times\sin G\). Substituting \(GH = 28\), \(FH = 40\) and \(\sin G = 1\), we get \(\sin F=\frac{28}{40}\times1=\frac{7}{10}=0.7\).

Step3: Find the angle

\(F=\sin^{- 1}(0.7)\approx44.4^{\circ}\)

Answer:

\(44.4^{\circ}\)