I cut a triangle ABC out of a piece of paper. I found out that sinA+sinB+sinC=5/2 and a/sinA=16. What is the triangle’s perimeter?

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Answer 1 · 2018-03-20T12:35:16

Permeter $=(a+b+c)=40$

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By sine rule for a $DeltaABC$ we have the relation

$a/sinA=b/sinB=c/sinC.....[1]$ ,

where $a,b,c$ are opposite sides of the angles $A,B,C$ respectively

Given $a/sinA=16.....[2]$

and $sinA+sinB+sinC=5/2.........[3]$

combining [1] and [2] we get

$a/sinA=b/sinB=c/sinC=16$

Hence

$sinA=a/16$

$sinB=b/16$

$sinC=c/16$

Inserting these in [3] we get

$a/16+b/16+c/16=5/2$

$=>(a+b+c)=5/2xx16=40$

So Perimeter $=(a+b+c)=40$