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What is the value of x in the diagram?

 

The diagram:

https://latex.artofproblemsolving.com/2/8/b/28b17b52fcef38528e8b5b98d94cd530c8ee2f7f.png

 Jan 3, 2021
 #1
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The triangle on the left is a 30-60-90 right triangle

 

Its height =   8 * sqrt (3)/2   =  4sqrt (3)   =  sqrt (48)

 

The triangle on the right is a 45-45-90  right triangle.....the altitude and  base of this triangle are equal  since both are opposite 45° angles

 

So....by the Pythagorean Theroem

 

x  =  sqrt  [ (sqrt (48) )^2  +  (sqrt (48))^2   ]  =   sqrt  [2 (48)^2 ]  =      48sqrt (2)

 

cool cool cool

 Jan 3, 2021

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