In triangle EFG, tan∠GEF = 22/7, and the altitude from E divides FG into segments of length 3 and 17.

Determine the area of triangle EFG.

Denote  the height to base FG by h, hits the base at the point K.

S=10*h

22/7=TAN(FEK+GEK)=(  3/h+17/h)/(1-51/(h^2))

The positive root of the quadratic equation

11h^2-70h-561=0

turns to be h=11

so the area is 110 (square units)

Rem: a high school textbook problem

Posted by Ady TZIDON on 2016-01-16 11:26:03