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?
To find the angle formed where the ladder rests on the house, we can use the inverse of sine.
First, we need to find the length of the ladder that extends from the base to the house. This is the side opposite to the angle we want to find.
Using the Pythagorean theorem, we can calculate the length of this side:
ladder length^2 = (distance from the base to the house)^2 + (height of the house)^2
ladder length^2 = 4^2 + 20^2
ladder length^2 = 16 + 400
ladder length^2 = 416
Taking the square root of both sides, we find:
ladder length ≈ √416
ladder length ≈ 20.4 feet
Now, we can use the inverse of sine to find the angle.
sine(angle) = (height of the house) / (ladder length)
sine(angle) = 20 / 20.4
Taking the inverse of sine of both sides, we find:
angle ≈ arcsin(20 / 20.4)
angle ≈ 60.8 degrees
Therefore, the approximate angle formed where the ladder rests on the house is 60.8 degrees.