Question

scarlett leans a 30 - foot ladder against a wall. if the ladder reaches 29.3 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 \(c = 30\) (length of the ladder) and the adjacent side \(a=29.3\) (height on the wall). We use the cosine ratio \(\cos\theta=\frac{a}{c}\).

Step2: Calculate the cosine value

Substitute \(a = 29.3\) and \(c = 30\) into the formula: \(\cos\theta=\frac{29.3}{30}\approx0.9767\).

Step3: Find the angle

Take the inverse cosine of \(0.9767\), \(\theta=\cos^{-1}(0.9767)\). Using a calculator, \(\theta\approx12.7^{\circ}\).

Answer:

\(12.7^{\circ}\)