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  if the sides of a triangle are in AP and the greatest angle of the triangle is double the smallest angle the ratio of the sides of the triangle is  
Asked by rushabh123 | 17 Feb, 2019, 08:22: PM
answered-by-expert Expert Answer
Let the sides of triangle are (x-d), x and (x+d) as shown in figure, which are in Arithmetic progression.
 
By cosine rule, we have,   (x-d)2 + x2 - 2(x-d)x cos2θ = (x+d)2 .................(1)
 
By simplifying the above eqn.(1), we get  begin mathsize 12px style x over d space equals space fraction numerator 2 open parentheses 2 minus cos space 2 theta close parentheses over denominator open parentheses 1 space minus space 2 space cos space 2 theta close parentheses end fraction space equals space alpha space end style....................(2)
Let RHS of eqn.(2) is α.  Hence x  = ( α × d )
 
Ratio of sides of triangle :  (x-d) : x : (x+d) = (α-1) : α : (α+1)
Answered by Thiyagarajan K | 17 Feb, 2019, 10:52: PM

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