Answer:
Rounded to the nearest tenth, the perpendicular distance from the end of the passage to either side of the mound is approximately 108.6 feet.
Step-by-step explanation:
To find the perpendicular distance \( x \) from the end of the passage to either side of the mound, we can use the Pythagorean theorem since the passage, the perpendicular distance and the radius of the circular mound form a right triangle.
Let \( r \) be the radius of the circular mound, which is half the diameter. So, \( r = \frac{250}{2} = 125 \) feet.
We'll denote the perpendicular distance \( x \).
Using the Pythagorean theorem:
\[ x^2 + 62^2 = r^2 \]
\[ x^2 + 62^2 = 125^2 \]
\[ x^2 = 125^2 - 62^2 \]
\[ x^2 = 15625 - 3844 \]
\[ x^2 = 11781 \]
\[ x = \sqrt{11781} \]
\[ x \approx 108.6 \]
Rounded to the nearest tenth, the perpendicular distance from the end of the passage to either side of the mound is approximately \( 108.6 \) feet.
