Question

Find the length of side x in simplest radical form with a rational denominator.

Answer 1

I labeled the sides and angle in the picture attached.
Steps:
The definition of cosine:
cos(B) = adj / hyp

cos(B) = a / c

Solve for c.
c = a / cos(B)

Substitute our values of each variable into the equation.

c = sqrt(7) / cos(60)
cos(60) = 1 / 2

c = sqrt(7) / (1/2)

Multiply the numerator by the reciprocal of the denominator.
c = sqrt(7) * 2

X = 2 * sqrt(7)