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?
12°
78°
34°
90°
To find the approximate angle formed where the ladder rests on the house, we can use the inverse function of sine.
Let's call the angle we are looking for A. According to the given information, we know that the opposite side of angle A is 20 feet (the length of the ladder) and the adjacent side is 4 feet (the distance from the base of the ladder to the house).
Using the formula for sine:
sin(A) = opposite/hypotenuse
sin(A) = 20/√(20^2 + 4^2)
sin(A) = 20/√(400 + 16)
sin(A) = 20/√416
sin(A) ≈ 20/20.39 ≈ 0.98
Using the inverse function of sine:
A ≈ sin^(-1)(0.98)
A ≈ 78.46°
Therefore, the approximate angle formed where the ladder rests on the house is 78°, which can be rounded to 78°.