Question

select the correct answer.
consider triangle efg.
what is the approximate measure of angle g?
a. 55.8°
b. 82.8°
c. 41.4°
d. 94.8°

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(e^{2}=f^{2}+g^{2}-2fg\cos E\). For finding \(\angle G\), we use the formula \(\cos G=\frac{EF^{2}+FG^{2}-EG^{2}}{2\cdot EF\cdot FG}\). Here, \(EF = 8\), \(FG=12\), \(EG = 10\).

$$ \cos G=\frac{8^{2}+12^{2}-10^{2}}{2\times8\times12} $$

$$ \cos G=\frac{64 + 144-100}{192} $$

$$ \cos G=\frac{108}{192}=0.5625 $$

Step2: Find the angle \(G\)

We know that if \(\cos G = 0.5625\), then \(G=\cos^{-1}(0.5625)\)
Using a calculator, \(G\approx55.8^{\circ}\)

Answer:

A. \(55.8^{\circ}\)