Question

skylar leans a 24 - foot ladder against a wall so that it forms an angle of 60° with the ground. whats the horizontal distance between the base of the ladder and the bottom of the wall? round your answer to the nearest hundredth of a foot if necessary.
answer attempt 1 out of 2
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Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 60^{\circ}\), the hypotenuse is the length of the ladder (\(24\) feet), and the adjacent side is \(x\) (the horizontal distance we want to find). So, \(\cos60^{\circ}=\frac{x}{24}\).

Step2: Solve for \(x\)

Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{x}{24}\). Cross - multiply: \(x = 24\times\frac{1}{2}\).

Answer:

\(12\)