Question

Two corners of a triangle have angles of `(5 pi )/ 8` and `( pi ) / 3`. If one side of the triangle has a length of `14`, what is the longest possible perimeter of the triangle?

Answer 1

`=206`

Explanation:

Let in `DeltaABC,/_A=pi/3,/_B=5pi/8`
`and /_C =(pi-pi/3-5pi/8)=pi/24`
So smallest angle `/_C=pi/24`
For having a triangle of largest perimeter , let the side of given length be the smallest side `c=14`
`a/sinA=c/sinC`
`:.a= (csinA)/sinC=14xxsin(pi/3)/sin(pi/24)~~92.9`

`b= (csinB)/sinC=14xxsin(5pi/8)/sin(pi/24)~~99.1`

So the largest possible perimeter
`a+b+c=92.9+99.1+14 =206`