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

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 .

Answer 2

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,
`√(256)`, to find what b is..

b=16

Thus, your answer.