A roof has cross section pictured below, that is a right triangle. The diagram shows the dimensions of this cross section. Which is the height h, of the roof?

Question

Answer 1

Answer 2

19 by 45 by 49 triangle

average side = (19+45+49)/2 = 113/2 = 56.5

area = sqr(56.5(56.5-49)(56.5-45)(56.5-19)

=sqr(56.5(7.5)(11.5)(37.5)

=about 427.48

=hb/2 = 49h/2

h = 2(427.48)/49 = 2(8.724) = 17.448 feet

It's very close to a right triangle, 49^2 almost = 19^2 + 45^2,

but assuming it is a right triangle

then 19x45/2 = area of the triangle = 427.5

49h/2 = 427.5

h = (2/49)(427.5) = about 17.449 feet in height