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 relation from trigonometry:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- The angle \(\theta = 52^\circ\)
- The height of the pyramid (opposite side) = 481 feet
- The hypotenuse is the length we want to find.
Rearranging the sine equation to find the hypotenuse gives:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Plugging in the values:
\[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
Now we need to calculate \(\sin(52^\circ)\). Using a calculator:
\[ \sin(52^\circ) \approx 0.788 \]
Now, substitute this value into the equation:
\[ \text{hypotenuse} = \frac{481}{0.788} \approx 609.5 \]
Rounding this to the nearest foot, we have:
\[ \text{hypotenuse} \approx 610 \text{ feet} \]
Therefore, the correct answer is 610 feet.
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