ANSWER
The correct answer is B.
EXPLANATION
The cosine rule can be used to find the relation for b.
According to the cosine rule:
[tex] {b}^{2} = {a}^{2} + {c}^{2} - 2ac \cos( B ) [/tex]We have that a=4 and c=5 and B=60°
We plug in these values to get:
[tex]{b}^{2} = {4}^{2} + {5}^{2} - 2(4)(5) \cos( 60 \degree ) [/tex]
[tex]{b}^{2} = 16+ 25 - 40 ( \frac{1}{2} ) [/tex]
[tex]{b}^{2} = 16+ 25 - 20[/tex]
Take positive square root.
[tex]b = \sqrt{25 + 16 - 20} [/tex]
The correct answer is B
