To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can utilize the sine function, which is defined as the ratio of the length of the opposite side to the hypotenuse in a right triangle.
In this case:
- The opposite side is the height of the pyramid, which is 481 feet.
- The angle is 52°.
We can set up the equation using the sine ratio:
\[ \sin(52°) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{481}{L} \]
Where \(L\) is the length from the bottom to the top of the pyramid (the hypotenuse). Rearranging this gives:
\[ L = \frac{481}{\sin(52°)} \]
Now, we need to calculate this:
\[ \sin(52°) \approx 0.788 \]
Plugging this value into the equation:
\[ L = \frac{481}{0.788} \approx 610.63 \]
Rounding to the nearest foot, we get \(L \approx 611\) feet.
Since the response options given differ from this result and may not include 611 feet, we note that:
- 610 feet is the closest available answer.
Thus, the correct response using the sine ratio to find the length from the bottom to the top of the pyramid to the nearest foot is:
610 feet.
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