Question

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.
answer attempt 2 out of 2
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Explanation:

Step1: Identify the trigonometric ratio

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

Step2: Calculate the value of \(\sin\theta\)

\(\sin\theta=\frac{26.2}{30}\approx0.8733\).

Step3: Find the angle \(\theta\)

To find \(\theta\), we use the inverse - sine function \(\theta=\sin^{- 1}(0.8733)\). Using a calculator, \(\theta\approx60.8^{\circ}\).

Answer:

\(60.8\)