A 15-foot ladder is leaning against a tree. The base of the ladder is 8 feet away from the tree base. Using the inverse of sine, what is the approximate angle between the ladder and the tree?
Let θ be the angle between the ladder and the ground. According to the problem, the opposite side is 15 feet (the ladder) and the adjacent side is 8 feet (the base of the ladder).
Since sine is defined as the opposite side divided by the hypotenuse, we have:
sin(θ) = opposite/hypotenuse = 15/√(15^2+8^2)
= 15/√(225+64) = 15/√289
Simplifying the denominator further, we get:
= 15/17
To find the angle θ, we need to take the inverse sine (also known as arc sine) of 15/17:
θ = arcsin(15/17)
Using a calculator, we find that θ is approximately 56.31 degrees.