To find the length from the bottom to the top of the pyramids, we can use the sine ratio, which is defined as:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this scenario, the original height of the pyramid is the "opposite" side (which is 481 feet), and the hypotenuse is the length from the bottom to the top (which we are trying to find).
Let \( L \) be the length of the hypotenuse. Thus, we can set up the equation as follows:
\[ \sin(52^\circ) = \frac{481}{L} \]
To solve for \( L \), we can rearrange this equation:
\[ L = \frac{481}{\sin(52^\circ)} \]
Now, we need to calculate \( \sin(52^\circ) \). From a calculator or trigonometric table:
\[ \sin(52^\circ) \approx 0.7880 \]
Now substituting this value back into the formula for \( L \):
\[ L = \frac{481}{0.7880} \approx 609.5 \]
Rounding to the nearest foot gives:
\[ L \approx 610 \text{ feet} \]
Thus, the correct answer is a. 610 feet.
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