Ina triangle abc a,b,a are given and c1,c2 are two values of the third side
c.The sum of the areas of two triangles with sides a,b,c1 and a,b,c2 is
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Step-by-step explanation:
From cosine rule we have
⇒c^2 −2bccosA+b^2 −a^2 =0
let c1 and c2 be the roots of the above equation.
The sum of the roots =c1 +c2 =2bcosA
Now, sum of area of two triangle=Δ=Δ1 +Δ2 = bc1 sinA+bc2 sinA/2
= b(c1+c2 )sinA/2
⇒△=b ^2 cosA sinA= b^2 sin2A /2
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