Question

the circular stone mound in Ireland called Newgrange has a diameter of 250 feet. A passage 62 feet long leads toward the center of the mound. Find the perpendicular distance x from the end of the passage to either side of the mound

Answer 1

To find the perpendicular distance x from the end of the passage to either side of the mound, we can use the Pythagorean theorem. The approximate value of x is 108.54 feet.

Step-by-step explanation:

To find the perpendicular distance x from the end of the passage to either side of the mound, we need to start by finding the radius of the mound. The diameter of the mound is given as 250 feet, so the radius is half of that, which is 125 feet.

Next, we can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the radius, the perpendicular distance x, and the length of the passage. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the hypotenuse is the radius (125 feet), one side is the length of the passage (62 feet), and the other side is the perpendicular distance x. So we have the equation: x^2 + 62^2 = 125^2.

Solving for x, we have: x^2 = 125^2 - 62^2. Evaluating this expression gives us: x^2 = 15625 - 3844. Therefore, x^2 = 11781. Finally, taking the square root of both sides gives us: x = sqrt(11781). Evaluating this expression gives us the approximate value of x as 108.54 feet.

Answer 2

the complete question in the attached figure

we know that
If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord (Segments of Chords Theorem)

therefore

AB*BC=DB*BE
AB=x
BC=x
DB=62
BE=250-62---------> BE=188 ft

so
x*x=62*188----------> x²=11656--------> x=√11656--------> x=107.96 ft

the answer is x=107.96 ft