The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.
What is the Law of Cosine?
The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As per the law of cosine, the measure of angle x can be written as,
[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]
Hence, the value of x is 117.8°. thus, the correct option is A.
Learn more about the Law of Cosine:
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