Question

question: liam leans a 18 - foot ladder against a wall. if the ladder reaches 17 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree. answer: answer input box with attempt 2 out of 2 and submit answer button

Explanation:

Step1: Identify the right - triangle relationship

We have a right - triangle where the hypotenuse is the length of the ladder ($c = 18$ feet) and the height on the wall is one of the legs ($a = 17$ feet). We want to find the angle $\theta$ between the ladder and the ground. We use the sine function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin\theta=\frac{17}{18}$.

Step2: Calculate the angle

We know that $\theta=\sin^{- 1}(\frac{17}{18})$. Using a calculator, $\sin^{-1}(\frac{17}{18})\approx70.8^{\circ}$.

Answer:

$70.8$