Answer:
C
Step-by-step explanation:
Since we are given three sides and we want to find an angle, we can use the law of cosines.
The law of cosines is given by:
[tex]b^2=a^2+c^2-2ac\cos(B)[/tex]
In this case, a = 3, b = 5, and c = 7. Therefore:
[tex](5)^2=(3)^2+(7)^2-2(3)(7)\cos(B)[/tex]
Evaluate:
[tex]25=58-42\cos(B)[/tex]
Therefore:
[tex]-42\cos(B)=-33[/tex]
Dividing both sides:
[tex]\displaystyle \cos(B)=\frac{33}{42}[/tex]
And by taking the inverse cosine of both sides:
[tex]\displaystyle \angle B=\cos^{-1}\Big(\frac{33}{42}\Big)=38.2132...\approx 38^\circ[/tex]
Our answer is C.
