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?

About 3.36 feet or about 40.3 inches

Step-by-step 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.