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5.3b: Pythagorean theorem - find missing side
First, we must name the sides of a right triangle.
We name each of the sides that meet at the right angle as a and b.
The third side is labeled as c.
C is always the hypotenuse.
It must always be the hypotenuse;
otherwise, the Pythagorean theorem or the formula we use
which is a squared + b squared = c squared
will not work if you do have the hypotenuse as c.
The way to identify which side of the hypotenuse is that
it is always directly across from your right angle.
In identifying where the right angle is
and then finding the side across labeling it c or hypotenuse,
you will ensure to always use the formula correctly.
When finding a leg with a Pythagorean Theorem,
you must first isolate
and then you will take the square root
which you are isolating is either an a squared, the b squared or the c squared.
So you are isolating one of the variables.
It is the variable that you do not know.
Example 1 asks us to find the missing side.
As stated above, it is always good to find
which side is the hypotenuse at the beginning.
Remember the hypotenuse can be found by locating the right angle
and then finding the side directly across and labeling it c.
The other two sides are not important on whether they are a or b.
We will therefore label the side
7 yards as a and the side 2 yards as b.
We now need to use the formula a squared + b squared = c squared.
We will plug in each of these values
into their locations in the formula.
This means that a or 7 yards will go in a spot and get squared.
We then will add b or 2 yards and square it as well.
This ends in finding c squared.
We then need to find the values, 7 squared is 49.
We add to this for 2 squared which is 4 and finally that equals c squared.
When we add 49 and 4, we get 53 equals c squared.
At this point, we have isolated the variable meaning that
the variable is on one side
and the number is on the other.
We now must take the square root of each side.
When we take the square root of each side,
the square root of c squared becomes c
and we type the square root of 53 into our calculator.
We will round to the 100s so we get an answer of 7.28 yards.
We will look at another example.
Once again, we are asked to find the missing side.
As always, we located the right angle.
We then locate the side directly across from it
to identify which side is c.
They have given as c in this equation
and so we will label it c.
It does not matter whether we label the other two sides a or b,
so we will label the blank one a and the other b.
We can now use the formula a squared + b squared = c squared.
We will now plug these values in.
We do not know a so it remains a squared.
We do know the value for b, it is 4
so we will square it and then this equals c squared which is 8 squared.
We calculate the values of each of these numbers.
This results in a squared + 16 = 64.
We now need to isolate the variable
so we subtract 16 from both sides.
We now have a squared alone on one side of the equation.
On the other side of the equation,
we have 64 - 16.
64 - 16 is 48.
We now have isolated the variable
so we can take the square root of both sides.
The square root of a squared is a.
The square root of 48 is 6.93 if we are rounding to the 100s.
Remember to include your units or the centimeters.
Remember in using the Pythagorean Theorem
to always locate the side c or the hypotenuse
and that it is directly located across from the right angle.
Then remember to find the leg that is missing,
we use the Pythagorean Theorem by first isolating the variable
and then taking the square root.