Question

Two corners of a triangle have angles of `(2 pi )/ 3` and `( pi ) / 6`. If one side of the triangle has a length of `17`, what is the longest possible perimeter of the triangle?

Answer 1

Largest possible perimeter of the triangle `=` 63.4449

Explanation:

Three angles of the triangles are `pi/6, pi/6, (2pi)/3`
Side `a=17`
`a/sin a=b/sin b=c/sin c`
`17/sin (pi/6)=b/sin(pi/6)=c/sin((2pi)/3)`
Side `b=17, c=(17*sin ((2pi)/3))/sin(pi/6)`
`c=(17*sin(pi/3))/sin(pi/6)=(17*(sqrt3/2))/(1/2)`
Side `c=17sqrt3`

`:.` Perimeter of the triangle `=17+17+17sqrt3=17(2+sqrt3)`
Perimeter `=` 63.4449