Question

1.) An architect is designing a house with steps to

the front door. For safety, the steps should not :
be steeper than 50 degrees. The entrance to the....
house is 4 feet off of the ground How far out
from the house do the steps need to start?

Answer 1

About 3.36 feet or about 40.3 inches

Explanation:

The tangent ratio tells you ...

Tan = Opposite/Adjacent

In this geometry, we want ...

tan(50°) = (4 ft)/(distance)

Solving for distance gives ...

distance = (4 ft)/tan(50°) ≈ 3.3564 ft ≈ 40.28 in

The steps need to start about 3.36 feet, or about 40.3 inches, out from the house.