In triangle ABC, BC=32, tanB=35, and tanC=14. Find the area of the triangle.
side AB is contained on the line
y = (3/5)x
side AC is contained on the line
y = -(1/4)(x -32) = (-1/4)x + 8
The x intersection of these lines is
(3/5)x = -(1/4)x + 8
[ 3/5 + 1/4] x = 8
[17/20]x =8
x = 8 *20 / 17 = 160 /17
And the y value at this point = (3/5)(160 /17) = 96/17 = the altitude...call this AD
[ABC] = (1/2) BC * AD = (1/2) 32 * 96/17 = 1536 / 17