A carpenter is constructing a straircase in a house. The distance from the first floor to the basement is 10.3 feet. The staircase will be 17.9 feet long. What angle do the stair make with the basement floor?
Mathematics · College · Tue Nov 03 2020
Answered on
Given:
The distance from the first floor to the basement is 10.3 feet.
The staircase will be 17.9 feet long.
Find the angle of the stair and the basement floor.
Solution:
The given statement can be pictured out as a right triangle, where the staircase is the hypotenuse, and the distance of the first floor to the basement is the opposite side. In order to find the angle of the stair and the basement floor, we apply the SOHCAHTOA rule, which states that sin = opposite over hypotenuse, cos = adjacent over hypotenuse, and tan = opposite over adjacent. Since we are given, the opposite side and the hypotenuse, we will use the trigonometric function sin.
sinθ = 10.3 /17.9
θ = sin^-1(10.3 /17.9)
θ =35.13°
The stair and the basement floor has the angle of 35.13°.