Step by step
The question
Question: find the missing side of a right triangle with leg 8 m and longest side 10 m.
1 Name the sides
The longest side is called the hypotenuse.
We call it c.
It is always across from the right angle.
The two shorter sides make the right angle.
We call them a and b.
The rule for every right triangle: a² + b² = c².
2 Put the numbers in
Now put the numbers in: a = 8 and c = 10.
3 Work out the squares
8² means 8 times 8.
That is 64.
10² means 10 times 10.
That is 100.
Write the squares: 64 + b² = 100.
4 Remove the 64
We want b² by itself.
The 64 is in the way.
To remove 64, we take away 64.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
64 and − 64 make zero.
Cross them out.
100 minus 64 is 36.
5 Take the square root
b² is 36.
So b times b is 36.
That means b is the square root of 36.
The square root of 36 is the positive number that times itself makes 36.
6 times 6 is 36.
So b = 6 m.
The missing side is 6 m.
6 Check
Let's check: put b = 6 m back.
First a² + b².
Now c².
Both are 100.
So b = 6 m is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: remove the 64.
Then: take the square root.
Last: check.