Question 570626: How do you find the area of a triangle with the sides 33,30 and 23. (I can NOT use Herons formula or the law of sine or cosines to find it btw. Its an extra credit problem and I need help : /
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! use the longest side as the base
the altitude (h) divides the triangle into two right triangles; a, h, 30 and b, h ,23
a + b = 33
a^2 + h^2 = 30^2
b^2 + h^2 = 23^3
three equations, three unknowns
subtracting 2nd and 3rd equations ___ a^2 - b^2 = 30^2 - 23^2 ___ (a + b)(a - b) = 371
dividing by 1st equation ___ a - b = 371 / 33
adding 1st equation ___ a - b + a + b = 33 + (371 / 33) ___ 2a = 1460 / 33
solve for a, then substitute back to find h
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