A triangle has sides A, B, and C. The angle between sides A and B is #pi/4# and the angle between sides B and C is #pi/12#. If side B has a length of 4, what is the area of the triangle?

1 Answer
Mar 16, 2017

Area=1.73#units^2#

Explanation:

First you can figure out the last angle of the triangle which is #(2pi)/3# (if it helps better the angles are #15, 45, and 120# degrees.)
then you can use the law of sines to figure out another side.
#sin((2pi)/3)/4=sin(pi/4)/x#
#x=(4sin(pi/4))/sin((2pi)/3)=3.27#
then do that again to find the last side
#sin((2pi)/3)/4=sin(pi/12)/x#
#x=(4sin(pi/12))/sin((2pi)/3)=1.20#
then you can use Heron's formula.
First find S
#S=(a+b+c)/2=4.24#
then substitute
#A=sqrt(s(s-a)(s-b)(s-c))#
#A=sqrt(4.24(4.24-1.20)(4.24-4)(4.24-3.27))=1.73#