Asked by Pooja
In Triangle ABC, AD is median. If AB is 8, BC is 18, AD is 7, find AC
Answers
Answered by
Reiny
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
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
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