Question

montraie leans a 30 - foot ladder against a wall. if the ladder reaches 26.2 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 know the length of the hypotenuse (ladder length \(c = 30\) feet) and the length of the opposite side (height on the wall \(a=26.2\) feet). We use the sine ratio \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin\theta=\frac{26.2}{30}\).

Step2: Calculate the angle

First, calculate \(\frac{26.2}{30}\approx0.8733\). Then, find \(\theta\) using the inverse - sine function. \(\theta=\sin^{- 1}(0.8733)\). Using a calculator, \(\theta\approx60.8^{\circ}\).

Answer:

\(60.8\)