Question 570626
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