To find the length from the bottom to the top of the pyramid (the slant height) using the sine ratio, you can use the following relationship:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- The height of the pyramid (the opposite side) is 481 feet.
- The angle \(\theta\) is 52°.
- The hypotenuse is the length from the bottom to the top of the pyramid, which we'll call \(L\).
Rearranging the sine formula gives us:
\[ L = \frac{\text{opposite}}{\sin(\theta)} = \frac{481}{\sin(52^\circ)} \]
Now we will calculate it:
- First, find \(\sin(52^\circ)\): \(\sin(52^\circ) \approx 0.7880\).
- Now, calculate the hypotenuse length \(L\):
\[ L \approx \frac{481}{0.7880} \approx 609.0 \text{ feet} \]
Rounding to the nearest foot gives \(610\) feet.
Therefore, the correct answer is 610 feet.