Question

Two corners of a triangle have angles of `(3 pi )/ 8` and `( pi ) / 4`. If one side of the triangle has a length of `14`, what is the longest possible perimeter of the triangle?

Answer 1

Per`=50.5838`

Explanation:

Three angles are `pi/4,(3pi)/8,(3pi)/8`
`a/sin a=b/sin b=c/sin c`
`a/sin (pi/4)=bsin ((3pi)/8)=c/sin ((3pi)/8)`
`14/sin ((3pi)/8)=14/sin (pi/4)`
`b=(14*sin ((3pi)/8))/sin(pi/4)`
`b=(14*0.9239)/0.7071=18.2919`
`c=(14*sin((3pi)/8))/sin(pi/4)`
`c=(14*0.9239)/0.7071=18.2919`
Perimeter `=14+18.2919+18.2919=50.5838`