To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can use the following relationship:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of elevation (52°),
- the opposite side is the height of the pyramid (481 feet),
- and the hypotenuse is the length we want to find.
We can rearrange the sine ratio formula to solve for the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the values we know:
\[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
Now we calculate \(\sin(52^\circ)\) (using a calculator):
\[ \sin(52^\circ) \approx 0.788 \]
Now we substitute this value into the equation:
\[ \text{hypotenuse} \approx \frac{481}{0.788} \approx 610.4 \]
Rounding this to the nearest foot gives us approximately 610 feet.
So the correct response is 610 feet.
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