Question

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

Answer 1

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

Answer 2

Answer:

The support post positioned 23 feet far from the front of the house

Step-by-step explanation:

According to Pythagoras Theorem

(Hypotenuse)² = (Base)² + ( Perpendicular)²

We need to find Base so arranging the equation will give us

(Base)² = (Hypotenuse)² -  ( Perpendicular)²

Taking under root on both sides

Base =  √(Hypotenuse)² -  ( Perpendicular)²

Base =  √ (625 - 100)

Base = √525

Base = 23 feet