the sides of a triangleare three consecutive natural numbers and its largest angle is twice the smallest one . determine the sides of the triangle ?

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Please find below the solution to the asked query:

Let us consider first and second termsxsinθ=x+2sin2θxsinθ=x+22sinθcosθcosθ=x+22x....iLet us consider first and third termsxsinθ=x+1sin3θxsinθ=x+13sinθ-4sin3θxsinθ=x+1sinθ3-4sin2θ3-4sin2θ=x+1x3-41-cos2θ=x+1x3-4+4cos2θ=x+1x4cos2θ=x+1x+14cos2θ=x+1+xx4cos2θ=2x+1xUsing i4x+22x2=2x+1x4x+224x2=2x+1x4x+22x=2x+1x2+4+4x=2x2+x2x2+x-x2-4-4x=0x2-3x-4=0x2-4x+x-4=0xx-4+1x-4=0x+1x-4=0x=-1 is not possible.x=4x+1=5x+2=6Hence sides of triangle are 4,5,6. 

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