To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we need to relate the height of the pyramid and the angle of elevation.
Given:
- Height (\(h\)) = 481 feet
- Angle (\(\theta\)) = 52°
The sine ratio relates the opposite side (height of the pyramid) to the hypotenuse in a right triangle:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, the opposite side is the height of the pyramid and the hypotenuse is the length from the base to the top (\(L\)). We can rearrange the sine formula to solve for \(L\):
\[ L = \frac{h}{\sin(\theta)} \]
Substituting the known values:
\[ L = \frac{481}{\sin(52°)} \]
Using a calculator, we find \(\sin(52°) \approx 0.7880\):
\[ L = \frac{481}{0.7880} \approx 609.02 \]
Rounding this to the nearest foot, we get:
\[ L \approx 610 \text{ feet} \]
Therefore, the correct answer is 610 feet.
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