Consider abc with the measure of angle b equal to 60 degrees, and side lengths a=4 and c=5. which option lists an expression that is equivalent to the length of side b?

For this case we can use the law of cosine to determine the length of side b.
 We have then:
 b ^ 2 = a ^ 2 + c ^ 2 - 2 * a * c * cos (B)
 Substituting values we have:
 b ^ 2 = 4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60)
 Clearing b:
 b = root (4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60))
 
 an expression that is equivalent to the length of side b is:
 b = root (4 ^ 2 + 5 ^ 2 - 2 * 4 * 5 * cos (60))

Step-by-step explanation:

(The choices are attached)

We don't if the triangle ABC is a right triangle of other kind, that's why we need to use the cosines law which is defined as

Where and , replacing these values we have

Remember that

Therefore, the second choice is the correct answer