These are similar triangles, because of the same Angle-Angle similarity test ( bottom right and top angles are the same as stated in the drawing). This means that the sides are proportional and can be solved with an equation of ratios as follows:

BE / DE = BC / AC

28 / 32 = BC / 48 (Substituting the given values for the side lengths)

48*28 / 32 = BC (Multiplying 48 to both sides)

42 = BC (Solving the multiplication and division)

ANSWER: Similar by Angle-Angle Similarity Test

BC = 42

Jan 11th, 2015

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