Answer:
[tex]\sqrt{32}[/tex]
Step-by-step explanation:
Pythagorean - [tex]a^2+b^2=c^2[/tex]
where a and b = legs and c = hypotenuse
For the following problem we are given the hypotenuse ( [tex]\sqrt{84}[/tex] ) and a leg ( [tex]\sqrt{52}[/tex] ) and we need to find the missing side length ( which also happens to be a leg.)
That being said we can find the missing leg by plugging in what we are given into [tex]a^2+b^2=c^2[/tex] ( let a = missing side length )
[tex]a^2+\sqrt{52}^2=\sqrt{84} ^2\\\sqrt{52} ^2=52\\\sqrt{84}^2 =84\\a^2+52=84[/tex]
* subtract 52 from each side
84 - 52 = 32
52 - 52 cancels out
we now have a² = 32
step 2 take the square root of each side
[tex]\sqrt{a^2} =a\\\sqrt{32} =\sqrt{32}[/tex]
Assuming that we are supposed to leave the answer in radical form the answer would be sqrt 32
