Question

a carpenter is constructing a staircase in a house. the distance from the first floor to the basement is 8.6 feet. the staircase will be 14.1 feet long. what angle do he stairs made with the basement floor?

Answer 1

theta = arctan(8.6 / 14.1) = 36.8 degrees

To find the angle the stairs make with the basement floor, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the distance from the first floor to the basement (8.6 feet) and the adjacent side is the length of the staircase (14.1 feet). So, the tangent of the angle is 8.6 / 14.1.

To find the angle itself, we can take the arctangent of the tangent of the angle. The arctangent is the inverse function of the tangent function. So, the angle is equal to arctan(8.6 / 14.1).

The arctangent of 8.6 / 14.1 is approximately 36.8 degrees. So, the stairs make an angle of approximately 36.8 degrees with the basement floor.