Question

A triangle has two corners with angles of `pi / 12` and `(7 pi )/ 8`. If one side of the triangle has a length of `3`, what is the largest possible area of the triangle?

Answer 1

A = 223.478

Explanation:

Sum of 3 amgles of a triangle is `pi`
So the third angle is `pi/24`
for the largest possible area the side needs to be taken as the smallest side
using sine rule `a/sinA =b/sinB=c/sinC`
taking a = 3
we get b = 5.949 and c = 8.796

using the formula for area of a triangle when 3 sides are given:
`A = sqrt(S*(S-a)*(S-b)*(S-c))`
where S is semiperimeter = 19.745
A = 223.478