The approximate measure of angle G is 41.4°. The correct option is C. 41.4°
Law of cosines
From the question, we are to determine the measure of angle G
From the law of cosines, we can write that
[tex]cos\ G =\frac{e^{2}+f^{2}-g^{2} }{2ef}[/tex]
In the diagram,
e = 12
f = 10
g = 8
Putting the values into the equation
[tex]cos\ G =\frac{12^{2}+10^{2}-8^{2} }{2\times 12 \times 10}[/tex]
[tex]cos\ G =\frac{144+100-64 }{240}[/tex]
[tex]cos\ G =\frac{180}{240}[/tex]
cosG = 0.75
G = cos⁻¹(0.75)
G = 41.4°
Hence, the approximate measure of angle G is 41.4°. The correct option is C. 41.4°
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