Question

question
as shown in the diagram below, the top of the slide is 12 feet from the ground and has an angle of depression of 53°. what is the length of the slide? round answer to the nearest foot.
answer attempt 1 out of 2
additional solution no solution
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Explanation:

Step1: Determine the trigonometric relationship

The angle of depression is \(53^{\circ}\). The height (opposite side) is \(12\) feet. Let the length of the slide (hypotenuse) be \(x\). Using the sine function: \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin(53^{\circ})=\frac{12}{x}\).

Step2: Solve for \(x\)

We know that \(\sin(53^{\circ})\approx0.7986\). Then \(x = \frac{12}{\sin(53^{\circ})}\). Substituting the value of \(\sin(53^{\circ})\), we get \(x=\frac{12}{0.7986}\approx15\).

Answer:

\(15\)