Question

question
nora leans a 22 - foot ladder against a wall. if the ladder reaches 20.4 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.
answer
attempt 1 out of 2
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Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse (\(c = 22\) feet) and the height on the wall is the opposite side (\(a=20.4\) feet) with respect to the angle \(\theta\) between the ladder and the ground. We use the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
So, \(\sin\theta=\frac{20.4}{22}\).

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

\(\frac{20.4}{22}=0.92727\cdots\)

Step3: Find the angle \(\theta\)

We know that \(\theta=\sin^{- 1}(0.92727)\). Using a calculator, \(\theta\approx68.0^{\circ}\)

Answer:

\(68.0^{\circ}\)