To find the length from the bottom to the top of the pyramid using the sine ratio, we can use the following formula:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- The angle \(\theta\) is 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 that we want to find (let's denote it as \(x\)).
Rearranging the formula gives us:
\[ x = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ x = \frac{481}{\sin(52°)} \]
Calculating \(\sin(52°)\):
\[ \sin(52°) \approx 0.788 \]
Now we can calculate \(x\):
\[ x \approx \frac{481}{0.788} \approx 609.29 \]
Rounding to the nearest foot, \(x \approx 609\) feet.
Thus, the answer that correctly uses the sine ratio to find the length from the bottom to the top of the pyramid to the nearest foot is 610 feet.