Question

brody leans a 22 - foot ladder against a wall. if the ladder reaches 20.8 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the ladder is the hypotenuse ($c = 22$) and the height on the wall is the opposite side ($a=20.8$) with respect to the angle $\theta$ (the angle between the ladder and the ground). We use the sine ratio: $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
So, $\sin\theta=\frac{20.8}{22}$.

Step2: Calculate the angle

First, calculate $\frac{20.8}{22}=0.945454\cdots$.
Then, find $\theta$ using the inverse - sine function: $\theta=\sin^{- 1}(0.945454\cdots)$.
Using a calculator, $\theta\approx71.0^{\circ}$.

Answer:

$71.0^{\circ}$