To find the length from the bottom to the top of the Great Pyramid of Giza using the sine ratio, we can use the height of the pyramid and the angle of elevation.
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In a right triangle, the sine of an angle is defined as the ratio of the opposite side (height of the pyramid) to the hypotenuse (the length from the bottom to the top of the pyramid).
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According to the problem, we have:
- Height (opposite side) = 481 feet
- Angle = 52 degrees
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The sine ratio can be expressed as: \[ \sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}} \] Replacing the variables, we have: \[ \sin(52^\circ) = \frac{481}{\text{hypotenuse}} \]
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To find the hypotenuse (length from the bottom to the top), we rearrange the equation: \[ \text{hypotenuse} = \frac{481}{\sin(52^\circ)} \]
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Using a calculator, we find \(\sin(52^\circ)\): \[ \sin(52^\circ) \approx 0.788 \]
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Now, we calculate the hypotenuse: \[ \text{hypotenuse} \approx \frac{481}{0.788} \approx 609.02 \]
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Rounding to the nearest foot, we find that the length from the bottom to the top of the pyramid is approximately 609 feet.
Looking at the choices provided:
- 610 feet
- 379 feet
- 781 feet
- 296 feet
The closest option is 610 feet.
1 answer