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?

1 Answer

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

Explanation:

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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#