Question

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

Explanation:

Step1: Apply the Law of Cosines

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

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

Step2: Calculate the numerator and denominator

First, calculate the numerator: \(8^{2}+12^{2}-10^{2}=64 + 144-100=108\).
The denominator: \(2\times8\times12 = 192\).
So, \(\cos G=\frac{108}{192}=0.5625\).

Step3: Find the angle

Take the inverse - cosine of \(0.5625\), \(G=\cos^{-1}(0.5625)\). Using a calculator, \(G\approx55.8^{\circ}\).

Answer:

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