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Find the exact value of x with rational denominator if the line passing through (x, 3) and (2, 1) makes an angle of 60(degrees) with the x-axis.

 

Thank you so much 

 Oct 6, 2017
 #1
avatar+27480 
+2

tan(60°) = (3 - 1)/(x - 2) → 2/(x - 2)

 

tan(60°) = sqrt(3)/2

 

So:  sqrt(3)/2 = 2/(x - 2)

 

x - 2 = 2*2/sqrt(3)

 

x = 2 + 4/sqrt(3) 

 

x = 2 + 4*sqrt(3)/3

 

x = (2*3 + 4*sqrt(3))/3  

 

x = (6 + 4*sqrt(3))/3

 Oct 6, 2017

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