Question

PLEASE HELP.

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?

Answer 1

(B)
`b=√(25+16-20)`

Explanation:

It is given that we have to consider triangle ABC in which ∠B=60° and the side lengths are a=4 and c=5.

Therefore, in order to find the value of the side length b, we will use the Law of Cosines that is:

`b^2=c^2+a^2-2(c)(a)cosB`

substituting the given values, we get

`b^2=(5)^2+(4)^2-2(5)(4)cos60^(\circ)`

`b^2=25+16-40((1)/(2))`

`b^2=25+16-20`

`b=√(25+16-20)`

which is the required side length of b.

Thus, option B is correct.

Answer 2

we know that
the law of cosines establish
b²=a²+c²-2*a*c*cos B
in this problem
a=4 units
c=5 units
B=60°
so
b²=a²+c²-2*a*c*cos B
b²=4²+5²-2*4*5*cos 60°
b²=16+25-40*(1/2)
b²=16+25-20
b=√[16+25-20]

the answer is
b=√[16+25-20]