Question

A triangle has two corners with angles of `pi / 2` and `(3 pi )/ 8`. If one side of the triangle has a length of `7`, what is the largest possible area of the triangle?

Answer 1

Area of the largest triangle possible `=87.4551`

Explanation:

The angles are `pi/2,(3pi)/8,pi/8`
It is a right angle triangle.

Smallest side `=7` It is also the height.
`:.a/sin(pi/12)=b/sin((3pi)/8)=c/sin(pi/2)`
`7/sin(pi/12)=b/sin((3pi)/8)=c/1`
`c=7/sin(pi/12)=27.0459=` hypotenuse of the triangle.
`b=((7*sin((3pi)/8))/sin(pi/12))`
`=24.9872`. It is also the base.

Area of the triangle`=(1/2)*b*h=(1/2)*7*24.9872=87.4551`