Question

nathan leans a 20-foot ladder against a wall. if the ladder reaches 18.9 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 ($c = 20$ feet) and the height on the wall is the opposite side ($a=18.9$ 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, $\sin\theta=\frac{18.9}{20}$.

Step2: Calculate the angle

We know that $\theta=\sin^{- 1}(\frac{18.9}{20})$.
First, calculate $\frac{18.9}{20}=0.945$.
Then, $\theta=\sin^{-1}(0.945)$.
Using a calculator, $\theta\approx70.9^{\circ}$.

Answer:

$70.9^{\circ}$