A ladder is resting against an outside wall of a building. The ladder is extended 23 feet, and reaches a distance of 17 feet up the wall.
Using the inverse of sine, what is the angle of elevation formed where the base of the ladder rests on the ground?
The angle of elevation can be calculated using the inverse sine function, which is also known as arcsine.
The angle of elevation, let's call it θ, is the angle between the ladder and the ground. It is opposite to the side of length 17 feet and adjacent to the side of length 23 feet.
Using the definition of sine, we have:
sin(θ) = opposite/hypotenuse
sin(θ) = 17/23
To find the angle θ, we can take the inverse sine of both sides:
θ = arcsin(17/23)
Using a calculator to evaluate arcsin(17/23), we find that θ ≈ 46.03 degrees.
Therefore, the angle of elevation formed where the base of the ladder rests on the ground is approximately 46.03 degrees.