Question

There is a circular park of radius 15 meters. Three friends Lillian, William, and Jacob are sitting at equal distance on its boundary each having a toy telephone (connected using strings) in their hands to talk to each other. Find the length of the string between the pair of the telephones.

Answer 1

15√3 meters ≈ 26 meters

Explanation:

The three boys are sitting at equal distances on the circle, so they form an equilateral triangle.

Draw one line cutting the triangle in half, and another line from one corner to the center of the circle. These two lines form a large 30-60-90 triangle on one side, and a smaller 30-60-90 triangle on the other side.

The hypotenuse of the smaller triangle is the radius of the circle, so the short leg is equal to 7.5 meters. That means the height of the equilateral triangle is 15 meters + 7.5 meters = 22.5 meters.

To find the side length of the equilateral triangle, we can either find the hypotenuse of the larger 30-60-90 triangle, or double the long leg of the smaller 30-60-90 triangle. Either way, it's 15√3 meters.