In Triangle ABC, AD is median. If AB is 8, BC is 18, AD is 7, find AC

Answer 1

Since AD is the median
BD = DC = 9
In ∆ABD, let ∢BDA = Ø
by the cosine law:
8^2 = 9^2 + 7^2 - 2(9)(7)cosØ
cosØ = .5238
Ø = 58.4°
the ∢ADC = 121.59°

now in ∆ADC
AC^2 = 49 + 64 - 2(7)(8)cos121.59
= 171.666667
AC = 13.102 or 13