Hello, ecdtrls516!

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

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 $\displaystyle B.$

The top of the bamboo (A) touches the ground 3 ft from C: .$\displaystyle AC = 3$

Let $\displaystyle h = BC$ (the height of the break).

Then: .$\displaystyle AB = 10-h$

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

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

. . . . . and solve for $\displaystyle h.$