To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can set up the following relationship based on the right triangle formed by the height of the pyramid and the length from the bottom to the top (the hypotenuse).
The sine ratio is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- \( \theta = 52^\circ \)
- The opposite side (height of the pyramid) = 481 feet
- The hypotenuse (length from the bottom to the top of the pyramid) = \( x \)
Therefore, we can write the equation as:
\[ \sin(52^\circ) = \frac{481}{x} \]
To find \( x \), we can rearrange the equation:
\[ x = \frac{481}{\sin(52^\circ)} \]
Now, we calculate \( \sin(52^\circ) \):
\[ \sin(52^\circ) \approx 0.7880 \]
Then we can substitute this value:
\[ x \approx \frac{481}{0.7880} \approx 610.28 \text{ feet} \]
Rounding to the nearest foot, the length from the bottom to the top of the pyramid is approximately 610 feet.
Thus, the correct response is:
610 feet.