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?

1 Answer
Oct 20, 2017

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