To find the length from the bottom to the top of the pyramid (the hypotenuse in this context) using the sine ratio, you can use the following relationship:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of the pyramid (52°)
- The "opposite" side is the height of the pyramid (481 feet)
- The "hypotenuse" is the length from the bottom to the top of the pyramid, which we want to find.
Rearranging the formula to solve for the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} = \frac{481}{\sin(52^\circ)} \]
Now, we can calculate \(\sin(52^\circ)\):
\(\sin(52^\circ) \approx 0.788\) (using a calculator)
Now, substitute the value into the equation:
\[ \text{hypotenuse} \approx \frac{481}{0.788} \approx 609.4 \]
Rounding to the nearest foot gives approximately 610 feet.
So, the correct response is 610 feet.