Question

Two corners of a triangle have angles of `( pi )/ 3` and `( pi ) / 6`. If one side of the triangle has a length of `15`, what is the longest possible perimeter of the triangle?

Answer 1

Longest possible perimeter `=70.98`

Explanation:

Given two angles are `pi/3=60^0` & `pi/6=30^0`
There the third angle `=180-60-30=90^0`
It is a right angle triangle with angles in the ratio of `1:2:3` and hence the sides in the ratio of `1:sqrt3:2` where the smallest side is 1. To get the longest perimeter, smallest side 1 should have the length 15.
Perimeter of the triangle is sum of all the three sides.
`=15+15sqrt3+(15*2)=15(1+sqrt3+2)`
`=15*(1+1.732+2)=15*4.732=70.98`