Question

The architect's side view drawing of a sandbox-style house shows a post that supports the roof ridge. The support post is 10 ft tall. How far from the front of the house is the support post positioned? (front to back is 25 ft)

Answer 1

Do you have a diagram that goes with this question?

Answer 2

yeah same?

Answer 3

I do but I'm not sure how to put it on here..

Answer 4

Best I could do, number 22.

Answer 5

Angles marked 1 are equal.
Angles marked 2 are equal.

Therefore, triangles ABD and CAD are similar.
BD / AD = AD / CD
AD^2 = BD * CD
10^2 = x * (25-x)
100 = 25x - x^2
x^2 - 25x + 100 = 0
x^2 - 20x - 5x + 100 = 0
x(x - 20) - 5(x - 20) = 0
(x-5)(x-20) = 0
x = 5 or x = 20
From the diagram we can see x = 5 ft. is the solution. x = 20 is an extraneous solution (represents length DC here) and can be discarded.

Answer: 5 feet.