To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can use the sine function in the following way:
The sine of an angle in a right triangle is given by the formula:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- The "opposite" side is the height of the pyramid (481 feet).
- The "hypotenuse" is the length we want to find.
- The angle \( \theta \) is approximately 52°.
Rearranging the formula to find the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
Now calculating \( \sin(52^\circ) \):
Using a calculator, \( \sin(52^\circ) \approx 0.7880 \).
Now we can calculate the hypotenuse:
\[ \text{hypotenuse} \approx \frac{481}{0.7880} \approx 609.2 \text{ feet} \]
Rounding to the nearest foot, we get approximately 610 feet.
Therefore, the correct answer is 610 feet.