The value of angle G will be approximately 41.4 °
What is law of cosine ?
The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.
c² = a² + b² - 2ab cos[tex]\rm \gamma[/tex]
Here in triangle EFG ,
To find angle G
a = 12
b=10
c=8
8² = 12² + 10² - 2*12*10 cos[tex]\rm \gamma[/tex]
64 = 144 + 100 -240 cos [tex]\rm \gamma[/tex]
64-244 = -240 cos[tex]\rm \gamma[/tex]
-180 = -240 cos[tex]\rm \gamma[/tex]
180/240 = cos [tex]\rm \gamma[/tex]
3/4 = cos [tex]\rm \gamma[/tex]
Therefore angle G will be approximately 41.4 °
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