To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can use the following relationship:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
In this case:
- \(\theta\) is the angle of the pyramid (52°)
- The "opposite" side is the height of the pyramid (481 feet)
- The "hypotenuse" is the length from the bottom to the top of the pyramid that we want to find.
Rearranging the sine formula to solve for the hypotenuse:
\[ \text{hypotenuse} = \frac{\text{opposite}}{\sin(\theta)} \]
Substituting the known values:
\[ \text{hypotenuse} = \frac{481}{\sin(52°)} \]
Calculating \(\sin(52°)\):
\[ \sin(52°) \approx 0.7880 \]
Now substituting that value into the equation:
\[ \text{hypotenuse} = \frac{481}{0.7880} \approx 609.0 \text{ feet} \]
Rounding to the nearest foot, we get approximately 610 feet.
Thus, the length from the bottom to the top of the Great Pyramid of Giza, to the nearest foot, is 610 feet.
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