Question

PLS help. 30 points and brainliest

Answer 1

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:

$b^2=a^2+c^2-2ac\cos(B)$

In this case, a = 3, b = 5, and c = 7. Therefore:

$(5)^2=(3)^2+(7)^2-2(3)(7)\cos(B)$

Evaluate:

$25=58-42\cos(B)$

Therefore:

$-42\cos(B)=-33$

Dividing both sides:

$\displaystyle \cos(B)=\frac{33}{42}$

And by taking the inverse cosine of both sides:

$\displaystyle \angle B=\cos^{-1}\Big(\frac{33}{42}\Big)=38.2132...\approx 38^\circ$

Our answer is C.