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°, 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

1 answer

To find the height from the top of the slide to the ground, we can use trigonometry. The angle of depression is given as 31.66°, and the length of the slide is 46 feet.

We can think of the slide as the hypotenuse of a right triangle, where:

  • The height from the top of the slide to the ground is the opposite side.
  • The angle at the top of the slide is 31.66°.
  • The hypotenuse (the slide) is 46 feet.

We can use the sine function, which is defined as:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]

So, we can express the height (opposite side) as:

\[ \text{height} = \text{hypotenuse} \cdot \sin(\theta) \]

Substituting in the known values:

\[ \text{height} = 46 \cdot \sin(31.66°) \]

Now, we will calculate the sine of 31.66° and then find the height:

\[ \sin(31.66°) \approx 0.5236 \quad (\text{using a calculator}) \]

Now, calculate the height:

\[ \text{height} = 46 \cdot 0.5236 \approx 24.0946 \text{ feet} \]

Rounding to the nearest foot, the height from the top of the slide to the ground is approximately:

\[ \text{height} \approx 24 \text{ feet} \]

Thus, the answer is 24 feet.