To find the length from the bottom to the top of the Great Pyramid of Giza, we can use the sine ratio in trigonometry. The sine of an angle in a right triangle is defined as the opposite side divided by the hypotenuse.
In this case:
- The height of the pyramid (481 feet) is the opposite side.
- The angle (52°) is the angle of elevation from the base to the top.
- We want to find the hypotenuse (the length from the bottom to the top).
Using the sine ratio:
\[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Substituting the known values:
\[ \sin(52^\circ) = \frac{481}{\text{hypotenuse}} \]
Let \( h \) be the hypotenuse. Rearranging gives:
\[ h = \frac{481}{\sin(52^\circ)} \]
Calculating \( \sin(52^\circ) \):
\[ \sin(52^\circ) \approx 0.788 \]
Now, substitute this value into the equation for \( h \):
\[ h \approx \frac{481}{0.788} \approx 609.66 \]
Rounding to the nearest foot gives us:
\[ h \approx 610 \text{ feet} \]
Therefore, the correct response is 610 feet.