To find the length from the bottom to the top of the pyramid (the slant height), you can use the sine ratio in a right triangle.
Given:
- The height (opposite side) = 481 feet
- The angle = 52 degrees
The sine of an angle in a right triangle is defined as the ratio of the length of the opposite side to the length of the hypotenuse (which, in this case, is the slant height \( h \)):
\[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case, we can write:
\[ \sin(52) = \frac{481}{h} \]
To find \( h \), we can rearrange the equation:
\[ h = \frac{481}{\sin(52)} \]
Now, we should calculate \( \sin(52) \):
\[ \sin(52) \approx 0.788 \]
Now substituting this value back into the equation:
\[ h \approx \frac{481}{0.788} \approx 610.3 \]
Rounding to the nearest foot, we find:
\[ h \approx 610 \text{ feet} \]
Therefore, the correct choice is:
610 feet.
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