BM = MC = x which is half of BC
angle AMB = T
then angle AMC = 180 - T
cos angle AMB = = cos T
cos angle AMC = cos(180-T)=-cos T
now law of cosines
4^2 = x^2 + 3^2 - 2(3x)cos T
8^2 = 3^2 + x^2 - 2(3x)(-cos T)
16 = x^2 + 9 - 6 x cos T
64 = x^2 + 9 + 6 x cos T
------------------------add
80= 2 x^2 + 18
2 x^2 = 62
x^2 = 31
x = sqrt 31
2x = BC = 2 sqrt 31
about 11.1
In triangle ABC, AB=4cm, AC=8cm and AM=3cm. AM is the median which meets BC and M. Then, BC is equal to
1 answer