Question

dalvin leans a 22-foot ladder against a wall. if the ladder reaches 20.1 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 ($c = 22$ feet) and the height on the wall is the opposite side ($a=20.1$ feet) 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, $\sin\theta=\frac{20.1}{22}$.

Step2: Solve for $\theta$

Take the inverse sine (arcsin) of both sides: $\theta=\sin^{- 1}(\frac{20.1}{22})$.
Using a calculator, $\frac{20.1}{22}\approx0.9136$.
Then $\theta=\sin^{-1}(0.9136)\approx66.1^{\circ}$.

Answer:

$66.1$