Question

alexander leans a 20-foot ladder against a wall. if the ladder reaches 18.7 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 triangle type and trigonometric ratio

We have a right triangle where the ladder is the hypotenuse (\(c = 20\) feet), the height on the wall is the adjacent side to the angle with the wall (\(a = 18.7\) feet), and we need to find the angle \(\theta\) between the ladder and the wall. We use the cosine ratio: \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Substitute the values and solve for \(\theta\)

Substitute \(a = 18.7\) and \(c = 20\) into the cosine formula: \(\cos\theta=\frac{18.7}{20}=0.935\). Then, take the inverse cosine: \(\theta=\cos^{-1}(0.935)\). Using a calculator, \(\theta\approx20.8^\circ\) (rounded to the nearest tenth).

Answer:

\(20.8^\circ\)