To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can use the formula for sine:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of 52°
- The opposite side is the original height of the pyramid, which is 481 feet
- The hypotenuse is what we want to find (the length from the bottom to the top of the pyramid).
Rearranging the sine formula to solve for the hypotenuse gives us:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the values:
\[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
Using a calculator to find \(\sin(52^\circ)\):
\(\sin(52^\circ) \approx 0.7880\)
Now, substituting this value back into the formula:
\[ \text{hypotenuse} \approx \frac{481}{0.7880} \approx 609.3 \]
Rounding to the nearest foot gives us approximately 610 feet.
Thus, the correct answer is 610 feet.
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