Question

question
dalvin leans a 28-foot ladder against a wall. if the ladder reaches 25.4 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.
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Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the ladder is the hypotenuse ($c = 28$ feet) and the height on the wall is the opposite side ($a=25.4$ feet) with respect to the angle $\theta$ that the ladder makes with the ground. We use the sine function: $\sin\theta=\frac{a}{c}$.

Step2: Calculate the sine of the angle

Substitute $a = 25.4$ and $c = 28$ into the sine formula: $\sin\theta=\frac{25.4}{28}\approx0.9071$.

Step3: Find the angle using the inverse sine function

$\theta=\sin^{- 1}(0.9071)$. Using a calculator, $\theta\approx65.1^{\circ}$.

Answer:

$65.1^{\circ}$