Problem involving pythagorean theorem

Question

There is a bamboo 10ft high, the upper end of which being broken reaches the ground 3ft from the stem. Find the height of the break.

Answer 1

To find the answer we first plug in the variables known into the pythagorean theorem (a²+b²=c²).  In this case the only one we know is a² which is 3, since that's how far from the stem the break fell.  We also know that the bamboo pole is 10 ft high total so "b" and "c" must equal 10ft.  The number for "c" must also be higher in value than "b" for the theorem to work.  By trying a few number combinations, I found the answer to be 3²+4.55²=5.45² ( 9+20.7025=29.7025 29.7025=29.7025).  This satisfies both the pythagorean theorem and "b" + "c" equaling the total height of bamboo at 10ft.