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: \[x \approx 24\]