Question

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?

Answer 1

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

Explanation:

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`