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In triangle ABC, AB = x cm, BC = (x+2)cm, AC = 5cm and ABC + 60 degrees 

Find the value of x

 Nov 11, 2017
 #1
avatar+98197 
+1

Using the Law of Cosines we have

 

5^2  =  x^2  +  (x + 2)^2  - 2[ x (x +2)] cos (60)

 

25  = x^2 + x^2 + 4x + 4 - 2 [x^2 + 2x] (1/2)

 

25 = 2x^2  + 4x + 4 - x^2 - 2x

 

25 = x^2 + 2x + 4   rearrange as

 

x^2 + 2x  - 21  =  0

 

Using the quadratic formula, x  = √22 - 1  ≈ 3.69

 

 

cool cool cool

 Nov 11, 2017

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