A triangle has sides A,B, and C. If the angle between sides A and B is #(3pi)/8#, the angle between sides B and C is #pi/12#, and the length of B is 5, what is the area of the triangle?

1 Answer
Apr 15, 2016

Hence area of triangle is #3.015# units

Explanation:

The length of side #B# is #5# and angle opposite this side is angle between sides #A# and #C#, which is not given. But as other two angles are #(3pi)/8# and #pi/12#, this angle would be

#pi-(3pi)/8-pi/12=(24pi-9pi-2pi)/24=(13pi)/24#

Now for using sine formula for area of triangle given by #1/2xxabxxsintheta#, we need one more side. Let us choose the side #C#, which is opposite the angle #(3pi)/8#.

Now using sine rule we have

#5/sin((13pi)/24)=C/sin((3pi)/8)# or #C=5xxsin((3pi)/8)/sin((13pi)/24)#

Hence area of triangle is #1/2xx5xx5xxsin((3pi)/8)/sin((13pi)/24)xxsin(pi/12)#

= #25/2xx(0.9239xx0.2588)/0.9914=3.015# units