Calculating the right angled triangle's cathetus We just started learning the Pythagorean theorem at school and we got a pretty difficult assignment. > 5 meter tall bamboo broke and the top of it touched the floor 2 meters from the base of the bamboo. What height did it break at? I've tried all sorts of different approaches, but I just can't get it right. I'm starting to think it's unsolvable. Am I missing something? Thanks! **Edit:** I've tried using the Pythagorean theorem (blue is the bamboo after it broke, gray is where the bamboo was before it broke): ![](

As you stated (I won't write the units of meters):

$$c+b=5, ~~~~~~~~~~~~~~~~~~~~~~ c^2=a^2+b^2.$$

You want to know either $c$ or $b$, so, you can write the first equation as $c=5-b$ or $b=5-c$. Now you can plug one of these into the second equation, and you would get an equation in terms of $a$ and $c$ or $b$, i.e. you CAN now solve for $b$ or $c$ and get the desired answer.