To find the length from the bottom to the top of the Great Pyramid of Giza, we can use the sine function in relation to the angle of elevation and the height of the pyramid.
In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse. Given that:
- The height of the pyramid (opposite side) = 481 feet
- The angle at the base = 52 degrees
- The hypotenuse (length from the bottom to the top of the pyramid) = \( L \)
We can set up the sine ratio as follows:
\[ \sin(52^\circ) = \frac{481}{L} \]
To find \( L \), we can rearrange the equation:
\[ L = \frac{481}{\sin(52^\circ)} \]
Now, we can calculate this using the sine of 52 degrees:
- Calculate \( \sin(52^\circ) \approx 0.7880 \) (using a calculator).
- Substitute this value into the equation:
\[ L \approx \frac{481}{0.7880} \approx 609.0 \]
Thus, rounding to the nearest foot, the length from the bottom to the top of the pyramid is approximately 609 feet.