The Sine and Cosine Ratios Quick Check 2 of 52 of 5 Items Question 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 781 feet 781 feet 296 feet 296 feet 379 feet 379 feet 610 feet 610 feet Skip to navigation page 21 of 21

1 answer

To find the length from the bottom to the top of the pyramid (the hypotenuse in this context) using the sine ratio, you can use the following relationship:

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

Where:

  • \(\theta\) 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, which we want to find.

Rearranging the formula to solve for the hypotenuse:

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

Now, we can calculate \(\sin(52^\circ)\):

\(\sin(52^\circ) \approx 0.788\) (using a calculator)

Now, substitute the value into the equation:

\[ \text{hypotenuse} \approx \frac{481}{0.788} \approx 609.4 \]

Rounding to the nearest foot gives approximately 610 feet.

So, the correct response is 610 feet.