Question

Find the missing value of a triangle one leg is 12 and the long side is 20 what is the other leg?

Answer 1

Simple,

using the Pythagorean Theorem...

$a^{2} + b^{2} = c^{2}$

You have the hypotenuse (C) and one of the legs (A)

So, plug in what you know...

$12^{2}+ b^{2} = 20^{2}$

144+$b^{2}$=400

Now,isolate $b^{2}$

$144+ b^{2} =400$
-144                   -144

Leaving you with...

$b^{2} =256$

So, now, $\sqrt{256}$, to find what b is..

b=16

Thus, your answer.

Answer 2

IF this is a 'right' triangle, then we can calculate an answer.
If it's NOT a right triangle, then no answer is possible.

I'm going to assume that it's a right triangle, because you did say
that one 'leg' is 12, and you want the length of the other 'leg'.   It's
common to refer to the two short sides of a right triangle as 'legs'.

In "Tales of Pythagoras", we learned that in a right triangle ...

                                            (Longest side)² = (one leg)²  +  (the other leg)²

In your triangle ...

                                               (20)²              =  (12)²  +  (the other leg)²

                                              (400)               =  (144) +  (the other leg)²

Subtract 144 from each side:  (The other leg)²  =  (400 - 144) = 256

                                             The other leg     =   √256  =  16 .