Isabell is standing at the top of a waterslide that leads to a pool below. The angle of depression from top of the slide to the pool is \( 31.66^{\circ} \), and the slide is 46 feet long. How far is the top of the slide from the ground? Round your answer to the nearest foot.
22 feet
24 feet
39 feet
72 feet

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Answer

Compute x and round to the nearest foot: \[x \approx 24\]

Steps

Step 1 ：Let x be the distance from the ground to the top of the slide. Use right triangle trigonometry and set up the equation: \[\tan(31.66^\circ) = \frac{x}{46}\]

Step 2 ：Solve the equation for x: \[x = 46\tan(31.66^\circ)\]

Step 3 ：Compute x and round to the nearest foot: \[x \approx 24\]

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