The original height of the Great Pyramid of Giza was 481 feet. The side of the pyramid rose at an angle of approximately 52° . Which of the following correctly uses the sine ratio to find the length from the bottom to the top of the pyramid to the nearest foot?(1 point) Responses 610 feet 610 feet 379 feet 379 feet 296 feet 296 feet 781 feet.

1 answer

To find the length from the bottom to the top of the pyramid using the sine ratio, we can use the relationship that the sine of an angle in a right triangle is equal to the opposite side divided by the hypotenuse.

The opposite side is the height of the pyramid (481 feet), and the angle is 52°. We are looking for the hypotenuse (the length from the bottom to the top of the pyramid).

Using the sine ratio, we have:

\[ \sin(52°) = \frac{\text{opposite}}{\text{hypotenuse}} \]

Substituting the known values, we get:

\[ \sin(52°) = \frac{481}{\text{hypotenuse}} \]

Now solving for the hypotenuse:

\[ \text{hypotenuse} = \frac{481}{\sin(52°)} \]

Calculating \(\sin(52°)\):

\[ \sin(52°) \approx 0.7880 \]

Now substituting this back into the equation:

\[ \text{hypotenuse} \approx \frac{481}{0.7880} \approx 609.4 \text{ feet} \]

Rounding this to the nearest foot gives us approximately 609 feet. Based on the options provided, the closest to this value is 610 feet.

Therefore, the correct answer is 610 feet.