Question 76929: WHAT IS THE FORMULA FOR FINDING ONE SIDE OF A RIGHT TRIANGLE IF ONE SIDE AND THE HYPOTENUSE ARE KNOWN?
Found 2 solutions by Edwin McCravy, bucky:
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
WHAT IS THE FORMULA FOR FINDING ONE SIDE OF A
RIGHT TRIANGLE IF ONE SIDE AND THE HYPOTENUSE ARE KNOWN?
_____________________________
UNKNOWN SIDE = Ö(HYPOTENUSE)² - (KNOWN SIDE)²
Edwin
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! You can still use the Pythagorean theorem:
.
The Pythagorean theorem says that if you square the lengths of the legs (short sides) of
a right triangle, the sums of these squares will equal the square of the hypotenuse
(long side) of the triangle. In equation form this becomes:
.
.
in which "a" and "b" are the lengths of the legs and "c" is the length of the hypotenuse.
.
This equation can be used to solve for an unknown side if the other two sides are known.
For example, suppose you are told that the length of the hypotenuse is 15 and the length of
one of the legs is 12. You can solve for the unknown leg. Just put these values into
the equation, but make sure you put them in the right place. In this example, the hypotenuse
is 15 so the 15 has to be put in the place of "c". You are also told that one of the
legs is 12. You can use it in place of either "a" or "b". Let's use it in the place of
"b". Then we will solve for the other leg "a". If we substitute these values in for
"b" and "c" the equation becomes:
.
.
Square out the two numbers ... square 12 and square 15 and you get:
.
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Since we are going to solve for "a" we need to eliminate the 144 on the left side. We
do that by subtracting 144 from the left side, but if we subtract something from one side
we also have to subtract it from the other side. So we subtract 144 from both sides and
the equation becomes:
.
.
and after doing the subtraction on the right side, the equation becomes:
.
.
Finally, you can solve for "a" by taking the square root of both sides to get:
.
.
If you really need the Pythagorean theorem written in a form that solves for one leg when you
are given the other leg and the hypotenuse, you can do that by starting with the equation:
.
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Assume that you know "b" and "c" ... one leg and the hypotenuse ... and you want to solve for
"a" ... the unknown leg. Begin by subtracting  from both sides to get:
.
.
Now to find "a" just take the square root of both sides and the result is:
.
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That's the equation for finding the leg "a" if the lengths of the hypotenuse "c" and the
other leg "b" are are known. However, it's probably easier just to remember that one
equation:
.
.
and plug the two known lengths into their appropriate position (making sure that the longest
side in the triangle is substituted for "c"). Then the rules for solving equations
can be used to solve for the missing quantity, just as we did above in solving for "a"
when we knew "b" was 12 and "c" was 15.
.
Hope this helps.
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