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If △ABC is an isosceles right triangle (45-45-90) with m∠C = 90° and AB = 20, find the EXACT value of side AC.

 Apr 27, 2020
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Turn that isoceles triangle on its side. 

Now you're looking at a right triangle with equal legs of 20 units 

 

By Pythagoras' Theorem, the hypotenuse of this triangle is the square root of ( 202 + 202

 

You can use your calculator to find the numerical approximation of the square root of 800

or if you want to be "exact" you can just call it 20 times sqrt(2) 

 

I don't know why the word EXACT in the problem was emphasized. 

You can't get an exact value because the square root of 2 is irrational. 

.

 Apr 27, 2020

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