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 ...
Let's call the angle of elevation at the base of the ladder $\theta$. According to the given information, the opposite side to this angle is 17 feet and the hypotenuse is 23 feet.
Using the inverse sine function (sin^(-1)), we can find the value of $\theta$ as:
$\theta = \sin^{-1} \left(\frac{ \text{opposite} }{ \text{hypotenuse} }\right) = \sin^{-1} \left(\frac{17}{23}\right)$
Using a calculator, we find that $\sin^{-1} \left(\frac{17}{23}\right) \approx 42$ degrees.
Therefore, the angle of elevation formed where the base of the ladder rests on the ground is approximately 42 degrees.