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In this example, we're asked to use the Pythagorean theorem to find the missing
side length for the given triangle. This is a right triangle
which means that it will satisfy the relationship
A^2 + B^2 = C^2.
Let's identify the sides here. This side is B
and this side is C. In this case we're looking for the link
of A. So let's set-up our Pythagorean Theorem as follows:
A^2 + B^2,
which is 3.8^2
equals C^2 which is 17.3^2
Let's multiply
our squares 3.8^2
is 14.44.
17.3^2
is 299.29.
Now we're going to do something a little bit different
so follow the steps closely. If I want
to determine A, I need to get A
by itself. I'm going to subtract
14.44 from both sides
of the equation. If I do that
on the left hand side I get A^2 + 0
which just leaves me A^2.
On the right hand side I get
284.85.
Once I'm at this step where I have
A^2 equals a number, I can take the square root
of both sides, which will turn A^2 into
A and 284.85
into the square root 284.85.
So the only time that you can really use this step
is if you have something squared equals a number.
You take the square root of both sides,
that eliminates the square,
and produces a square-root
over your number. So if I take that square root
and round it to the tenths place, I get 16.9
and in this case we have units so
that would be a length of 16.99 meters.
If you wanted to
check that the values are correct
you could plug in A^2 + B^2
equals C^2 and see if you get
approximately the same result.