The architects side view drawing of a saltbox-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?

The distance between the front and the back of the house is 25 ft

These calculations are based on the drawing of the file enclosed.

There are three right triangles.

From the big right triangle:

a^2 + b^2 = 25^2

From the small right triangle on the left side:

(25-x) ^2 + 10^2 = a^2

From the small right triangle on the right side

x^2 + 10^2 = b^2

=> (25-x) ^2 + 10^2 + x^2 + 10^2 = a^2 + b^2

=> (25-x) ^2 + 10^2 + x^2 + 10^2 = 25^2

=> 25^2 - 50x + x^2 + 10^2 + 10^2 = 25^2

=> x^2 - 50x + 100 = 0

Use the quadratic formular to find the roots:

x = 2.1 and x = 47.9

Distance from back: 25 - 2.1 = 22.9 ft

Answer: 22.9 ft