Three towns in a rural flat area of Colorado are each 12 miles from the other two.

Mr. P is in a hot air balloon.   At a certain point, he is exactly 7 miles from each of the towns.

Can you determine the height of the balloon?
Show your work.


Solution to the Problem:


The hot air balloon is one mile high.

The three towns are at the vertices of an equilateral triangle with a 12 mile side.

Use the 30-60-90 triangle to determine that the center of the triangle is 4√3 miles from each city.   I labeled it as 12 /√3 in the diagram below.

The height of the balloon hovering above is the third side of a right triangle in which one leg is 4√3 miles and the hypotenuse is 7 miles.

So, 72 = h2 + (4√3)2
49 = h2 + 48
Therefore, h = 1 mile




Here is Ritwik Chaudhuri's excellent solution which uses trigonometry:


Click here for Colin Bowey's excellent solution


Correctly solved by:

1. Colin (Yowie) Bowey Beechworth, Victoria, Australia
2. K. Sengupta Calcutta, India
3. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
4. Pedro Medina Central High School,
Grand Junction, Colorado
5. Davit Banana Istanbul, Turkey
6. Ritwik Chaudhuri Santiniketan, West Bengal, India
7. Kelly Stubblefield Mobile, Alabama