Given:
In triangle [tex]ABC, AB=9,BC=4,AC=7[/tex].
To find:
The measure of angle C.
Solution:
We have, [tex]AB=9,BC=4,AC=7[/tex]. It means [tex]c=9,a=4,b=7[/tex].
According to the law of cosines:
[tex]cos C=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
[tex]cos C=\dfrac{4^2+7^2-9^2}{2(4)(7)}[/tex]
[tex]cos C=\dfrac{16+49-81}{56}[/tex]
[tex]cos C=\dfrac{-16}{56}[/tex]
Taking cos inverse on both sides, we get
[tex]C=cos^{-1} \dfrac{-16}{56}[/tex]
[tex]C=106.60155[/tex]
[tex]C\approx 106.6[/tex]
Therefore, the correct option is C.
