A water-park slide covers 100 feet of horizontal space and is 36 feet high. A new replacement slide will create an angle with the water surface that measures twice that of the original slide. The new slide will use the same horizontal space as the old slide. What is the height of the new slide to the nearest foot? (Enter only the number.)

tan(theeta)=36/100

Theeta= tan-1(36/100)
Angle= 19.7

To find the height of the new slide, we can use the concept of trigonometry.

Let's first find the angle of the original slide. We know that the opposite side is 36 feet (height) and the adjacent side is 100 feet (horizontal distance). To find the angle θ, we can use the inverse tangent function (tan⁻¹):

θ = tan⁻¹(opposite/adjacent)
θ = tan⁻¹(36/100)

Using a calculator, we find that θ is approximately 20.56 degrees.

Since the new slide creates an angle that is twice that of the original slide, the new angle is 2 * 20.56 = 41.12 degrees.

Now, we can find the height of the new slide. We know the angle and the adjacent side (100 feet), and we need to find the opposite side (height). Again, we can use trigonometry:

height = adjacent * tan(θ)
height = 100 * tan(41.12)

Using a calculator, we find that the height of the new slide is approximately 87 feet (rounded to the nearest foot).