Given:
In triangle ABC, a=74.1, b= 60.8, c=114.2.
To find:
The measure of angle C.
Solution:
According to the Law of cosine:
[tex]\cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
Substituting [tex]a=74.1,b= 60.8,c=114.2[/tex], we get
[tex]\cos C=\dfrac{(74.1)^2+(60.8)^2-(114.2)^2}{2(74.1)(60.8)}[/tex]
[tex]\cos C=\dfrac{5490.81+3696.64-13041.64}{9010.56}[/tex]
[tex]\cos C=\dfrac{-3854.19}{9010.56}[/tex]
[tex]\cos C=-0.42774145[/tex]
Taking cos inverse on both sides, we get
[tex]C=\cos^{-1}{-0.42774145}[/tex]
[tex]C=115.324312[/tex]
[tex]C=115.3^\circ[/tex]
Therefore, the correct option is d.
