To find the length from the bottom of the pyramid to the top using the sine ratio, we can use the definition of sine in a right triangle.
In this case, you have the height of the pyramid (the opposite side, which is 481 feet) and the angle of elevation (52 degrees). We want to find the length of the hypotenuse (the length of the slant height from the base to the top).
The sine ratio is defined as follows:
\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \]
Where:
- \(\theta\) is the angle of elevation (52 degrees),
- the opposite side is the height of the pyramid (481 feet),
- the hypotenuse is what we want to find (let's call it \(x\)).
Using this information, we can set up the equation:
\[ \sin(52^\circ) = \frac{481}{x} \]
To find \(x\), we can rearrange the equation:
\[ x = \frac{481}{\sin(52^\circ)} \]
Now, you can calculate \(x\):
- Calculate \(\sin(52^\circ)\).
- Divide 481 by the result.
Using a calculator:
\[ \sin(52^\circ) \approx 0.7880 \]
Now substitute this value into the equation:
\[ x \approx \frac{481}{0.7880} \approx 609.86 \]
Rounding to the nearest foot, the length from the bottom of the pyramid to the top is approximately \(610\) feet.