BC = 4 centimeters,

m A = 20°

AC = ?

since

m A + m B + m C = 180

and also

m B = m C

we have

m A + m B + m B = 180

2 m B = 180 - m A

m B = (1/2)(180 - m A)

m B = (1/2)(180 - 20)

m B = 80°

using the The Law of Sines we have

BC/sin m A = AC/sin m B

AC = BC sin m B / sin m A

AC = 4 * sin(60)/sin(20)

AC = 10.13 cm rounded to two decimal places

click here to see the step by step calculation: