The length of the blue line labeled r in the image is [tex]\sqrt{a^2+b^2}[/tex]
In order to get the length of the blue line as shown in the diagram, we will use the formula for calculating the Pythagoras theorem:
The theorem states that the square of the hypotenuse (longest side) is equal to the sum of the square of the other two sides.
From the diagram shown:
Hypotenuse = r
The other two sides = 'a' and 'b'
According to the theorem
[tex]r^2=a^2+b^2[/tex]
Take the square root of both sides
[tex]\sqrt[]{r^2} =\sqrt[]{a^2+b^2}\\r= \sqrt[]{a^2+b^2}\\[/tex]
Hence the length of the blue line in the image is [tex]\sqrt{a^2+b^2}[/tex]
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