SOLUTION: 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 ne

Algebra ->  Triangles -> SOLUTION: 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 ne      Log On


   

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) About Me  (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