Step by step
The question
Question: find the missing side of a right triangle with leg 40 m and longest side 41 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 = 40 and c = 41.
3 Work out the squares
40² means 40 times 40.
That is 1600.
41² means 41 times 41.
That is 1681.
Write the squares: 1600 + b² = 1681.
4 Remove the 1600
We want b² by itself.
The 1600 is in the way.
To remove 1600, we take away 1600.
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.
1600 and − 1600 make zero.
Cross them out.
1681 minus 1600 is 81.
5 Take the square root
b² is 81.
So b times b is 81.
That means b is the square root of 81.
The square root of 81 is the positive number that times itself makes 81.
9 times 9 is 81.
So b = 9 m.
The missing side is 9 m.
6 Check
Let's check: put b = 9 m back.
First a² + b².
Now c².
Both are 1681.
So b = 9 m is right!
Let's look back.
First: name the sides.
Then: put the numbers in.
Then: work out the squares.
Then: remove the 1600.
Then: take the square root.
Last: check.