# [SOLVED] Right Triangle Problem.

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• Sep 21st 2007, 12:05 PM
ecdtrls516
[SOLVED] Right Triangle Problem.
I really need a formula on how this is calculated. A 10-ft-long stem of bamboo is broken in such a way that its tip touches the ground 3ft. from the base of the stem. What is the height of the break. The answer is 4.55ft, but how is this calculated using the pythagorean theorem (a^2 +b^2 = c^2) given only 1 variable (a) and the sum of b and c? Please help and give detailed response. Thank You!
• Sep 21st 2007, 12:26 PM
Soroban
Hello, ecdtrls516!

I don't suppose you made a sketch . . .

Quote:

A 10-ft-long stem of bamboo is broken in such a way
that its tip touches the ground 3 ft from the base of the stem.
What is the height of the break.

The answer is 4.55 ft

Code:

```    B *       | \       |  \     h |    \ 10-h       |      \       |        \   - - * - - - - - * - -       C    3    A```

The break is at $B.$
The top of the bamboo (A) touches the ground 3 ft from C: . $AC = 3$

Let $h = BC$ (the height of the break).
Then: . $AB = 10-h$

Now apply Pythagorus: . $BC^2 + AC^2 \:=\:AB^2$

So we have: . $h^2 + 3^2 \:=\:(10-h)^2$

. . . . . and solve for $h.$