Question

A triangle has sides A, B, and C. The angle between sides A and B is `(7pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 8, what is the area of the triangle?

Answer 1

Area of `Delta ABC = **196.0188**`

Explanation:

Three angles are `((7pi)/12, pi/12, pi/3)`

`C/ sin (/_C ) = A / sin( /_A ) = B / sin ( /_B)`
`C/ sin ((7pi)/12)= A / sin (pi / 12) = 8 / sin (pi/3)`

`C= (8 * sin ((7pi)/12))/sin (pi/3) = 8.9228`

`A = (8 * sin (pi/12))/sin (pi/3) = 2.3909`

Semi Perimeter of `Delta ABC s = (8 + 8.9228 + 2.3909)/2`
`s = 19.3137`
`s - a = 19.3137- 2.3909 = 16.9228`
`s - b = 19.3137 - 8 = 11.3137`
`s - c = 19.3137 - 8.9228 = 10.3909`

Area of `Delta ABC = sqrt(s(s-a)(s-b)(s-c))`

Area of `Delta ABC = sqrt (19.3137*16.9228*11.3137*10.3909)`
= 196.0188