Question

A 70 foot pole stands vertically in a horizontal plane supported by three 490 foot wires, all attached to the top of the pole. Pulled and anchored to three equally spaced points in the plane. How many feet apart are any two of those anchor points?

Answer 1

Find the radius formed by the distance between the pole and the wire:

The radius, the pole and the wire formed a right angle triangle

a² + b² = c²

70² + radius² = 490²

4900 + radius² = 240100

radius² = 240100 - 4900

radius² = 235200

radius = 484.97 ft

Find the circumference formed by the anchor points:

Circumference = 2πr

Circumference = 2π(484.97) = 3048.41 ft

Find the distance between two anchors:

Distance between 2 anchors = 3048.41 ÷ 3 = 1016.14 ft

Answer: The distance between two anchors is 1016.14 ft

Answer 2

Answer:

840ft

Step-by-step explanation:

The wires will be equally space at the circumference of a circle in the plane as shown in the figure above.

The three points will form an equilateral triangle, with the sides of the triangle equal to the shortest distance between the points.

Let the side of the triangle be ‘a’.

‘r’ is the radius of the circum-circle of the given triangle

Thus, a = √3 r ---(1)

 Now,

4902 = r2 + 702

r2= 702(72 – 1)

r2 = 702(48)

r = 70(4√3) = 280√3, putting in (1)

a = √3 * 280√3

= 840 ft = distance between the points