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°
90°
78°
78°
12°
12°
34°
34°
To find the angle formed where the ladder rests on the house, we can use the inverse sine function. In this case, we know the opposite side (the height of the house) and the hypotenuse (the length of the ladder).
Let's call the angle we're trying to find theta (θ). According to the sine function:
sin(θ) = opposite/hypotenuse
The opposite side is the height of the house, which is 20 feet, and the hypotenuse is the length of the ladder, which is 20 feet.
sin(θ) = 20/20
sin(θ) = 1
To find θ, we can take the inverse sine of 1:
θ = arcsin(1)
Using a calculator, we find that θ is approximately 90°.
Therefore, the approximate angle formed where the ladder rests on the house is 90°.