# Pythagoras CHAM SHER MIN, BETH S1-G
Get Started. It's Free Pythagoras ## 3. real life application

### 3.4. architects and engineers use this formula extensively when building ramps:

3.4.1. The owners of a house want to convert a stairway leading from the ground to their back porch into a ramp. The porch is 3 feet off the ground, and due to building regulations, the ramp must start 12 feet away from the base of the porch. How long will the ramp be?

3.4.2. To solve a problem like this one, it often makes sense to draw a simple diagram showing the legs and hypotenuse of the triangle.

3.4.3. :U07_L2_T1_tt_img6.png

3.4.4. Looking at the diagram, we can identify the legs and the hypotenuse of the triangle in the problem we need to solve. We know that the triangle is a right triangle since the ground and the raised portion of the porch are perpendicular—this means we can use the Pythagorean Theorem to solve this problem. We are given the lengths of legs a and b, so we can use that information to find the length of c, the hypotenuse.

3.4.5. Example

3.4.6. Problem

3.4.7. Find c when a = 3 and b =12

3.4.8. Pythagorean Theorem

3.4.9. Substitute known values in for a and b.

3.4.10. Simplify

3.4.11. Combine like terms

3.4.11.1. =

3.4.12. Take the square root of both sides

3.4.14. 12.37 ≈ c

3.4.15. The ramp will be just about 12.37 feet long.