To find the length from the bottom to the top of the pyramid (the hypotenuse of the right triangle formed by the height and the side length of the pyramid), you can use the sine ratio, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the opposite side is the height of the pyramid (481 feet), and the angle θ is 52°. You are solving for the hypotenuse (the length from the bottom to the top of the pyramid).
Rearranging the sine ratio gives you:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
Now, calculating \( \sin(52^\circ) \):
\[ \sin(52^\circ) \approx 0.7880 \]
Now plugging this value into the equation:
\[ \text{hypotenuse} = \frac{481}{0.7880} \approx 610.28 \]
Rounding to the nearest foot gives approximately 610 feet.
So, the correct answer is:
610 feet