Question

A triangle has sides A,B, and C. If the angle between sides A and B is `pi/12`, the angle between sides B and C is `pi/12`, and the length of B is 5, what is the area of the triangle?

Answer 1

Area of triangle = 3.0026

Explanation:

`/_A=pi/12, /_C=pi/12, /_B=(5pi)/6`
Side `B=5`
We know,`A/sin A=B/sin B=C/sin C`
`A/sin (pi/12)=5/sin ((5pi)/6)=C/sin (pi/12)`
`A=(5*sin (pi)/12)/sin ((5pi)/6)~~2.5881`
As `/_A=/_C, /_C~~2.5881`

`s=(A+B+C)/2=(5+2.5881+2.5881)/2=5.0881`
`s-A=s-C=5.0881-2.5881=2.5`
`s-B=5.0881-5=0.0881`

Area of triangle = `sqrt(s*(s-A)(s-B)(s-C))`
`=sqrt(5.0881*2.5881*0.0881*2.5881)=~~3.0026`