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? Round your answer to the nearest whole degree.
the answer is not 43
To find the angle of elevation, we can use the inverse sine function.
Let's call the angle of elevation θ.
We know that the opposite side to the angle is 17 feet and the hypotenuse (the ladder) is 23 feet.
Using the definition of sine, we have:
sin(θ) = opposite / hypotenuse
sin(θ) = 17 / 23
To find θ, we can take the inverse sine of both sides:
θ = sin^(-1)(17 / 23)
Using a calculator, this gives us:
θ ≈ 43.6 degrees
Rounding to the nearest whole degree, the angle of elevation formed where the base of the ladder rests on the ground is approximately 44 degrees.