Question

damian leans a 20-foot ladder against a wall. if the ladder reaches 17.7 feet up the wall, what angle does it form with the wall? round your answer to the nearest tenth of a degree.

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the hypotenuse (length of the ladder) \(c = 20\) feet and the adjacent side (height on the wall) \(a=17.7\) feet. We use the cosine ratio \(\cos\theta=\frac{a}{c}\).

Step2: Calculate the cosine of the angle

Substitute \(a = 17.7\) and \(c = 20\) into the formula: \(\cos\theta=\frac{17.7}{20}=0.885\).

Step3: Find the angle

Take the inverse cosine (arccos) of \(0.885\). Using a calculator, \(\theta=\cos^{-1}(0.885)\).

Answer:

\(\theta\approx27.7^{\circ}\)