Question

in triangle abc, a line parallel to AC intersects at AB at D and BC at E . If db is 6, ad is 2 and bc is 24, find de if ab and bc include a 60 degree angle

Answer 1

by the cosine law:
AC^2 = 8^2 + 24^2 - 2(8)(24)cos60°
= 448
AC = √448 = 8√7

now by similar triangles:
DE/8√7 = 6/8
DE = 48√7/8 = 6√7