Question

fawzia leans a 16-foot ladder against a wall. if the ladder reaches 15.7 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 know the hypotenuse (\(c = 16\) feet) and the adjacent side (\(a=15.7\) feet) with respect to the angle \(\theta\) (the angle between the ladder and the wall). We use the cosine ratio: \(\cos\theta=\frac{a}{c}\).

Step2: Substitute the values

Substitute \(a = 15.7\) and \(c = 16\) into the cosine formula: \(\cos\theta=\frac{15.7}{16}=0.98125\).

Step3: Find the angle

To find \(\theta\), we take the inverse - cosine (arccos) of \(0.98125\). So, \(\theta=\arccos(0.98125)\). Using a calculator, \(\theta\approx11.0^{\circ}\).

Answer:

\(11.0^{\circ}\)