Romeo owns a business that puts up and takes down holiday lights. He is working on a house and places the base of his 20-foot ladder at a 4-foot distance from the house. Using the inverse of sine, what is the approximate angle formed where the ladder rests on the house?
90,34,12,78
The angle formed where the ladder rests on the house can be approximated using the inverse of sine.
First, we need to determine the length of the ladder that is in contact with the house. We can do this by using the Pythagorean theorem:
(Length of ladder)^2 = (Distance from the house)^2 + (Height of the ladder)^2
(Length of ladder)^2 = 4^2 + 20^2
(Length of ladder)^2 = 16 + 400
(Length of ladder)^2 = 416
Length of ladder ≈ √416
Now, we can use the inverse of sine to find the angle:
Angle = sin^(-1) (Height of the ladder / Length of ladder)
Angle ≈ sin^(-1) (20 / √416)
Using a calculator, sin^(-1) (20 / √416) is approximately equal to 34.
Therefore, the approximate angle formed where the ladder rests on the house is 34 degrees.