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

379 feet
379 feet

781 feet
781 feet

296 feet
296 feet

610 feet

1 answer

To find the length from the bottom to the top of the Great Pyramid of Giza, we can use the sine ratio in trigonometry. The sine of an angle in a right triangle is defined as the opposite side divided by the hypotenuse.

In this case:

  • The height of the pyramid (481 feet) is the opposite side.
  • The angle (52°) is the angle of elevation from the base to the top.
  • We want to find the hypotenuse (the length from the bottom to the top).

Using the sine ratio:

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

Substituting the known values:

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

Let \( h \) be the hypotenuse. Rearranging gives:

\[ h = \frac{481}{\sin(52^\circ)} \]

Calculating \( \sin(52^\circ) \):

\[ \sin(52^\circ) \approx 0.788 \]

Now, substitute this value into the equation for \( h \):

\[ h \approx \frac{481}{0.788} \approx 609.66 \]

Rounding to the nearest foot gives us:

\[ h \approx 610 \text{ feet} \]

Therefore, the correct response is 610 feet.