Question

A triangle has sides A, B, and C. If the angle between sides A and B is `(pi)/3`, the angle between sides B and C is `(7pi)/12`, and the length of B is 7, what is the area of the triangle?

Answer 1

`=79.16`

Explanation:

This is a triangle where side `B=7` is opposite of the
Angle [`pi-(pi/3+7pi/12)]=pi-11pi/12=pi/12`
Therefore
`B/sin(pi/12)=C/sin(pi/3)`
or
`7/sin(pi/12)=C/sin(pi/3)`
or
`C=7sin(pi/3)/(sinpi/12)`
or
`C=7(3.34)`
or
`C=23.42`
`Height` of the triangle is `=7sin(pi-7pi/12)=7sin (5pi/12)=6.76`
Therefore
Area of the triangle`=1/2(C)(Height)`
`=1/2(23.42)(6.76)`
`=79.16`