A triangle has sides A, B, and C. Sides A and B have lengths of 3 and 5, respectively. The angle between A and C is #(5pi)/8# and the angle between B and C is # (pi)/12#. What is the area of the triangle?

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Answer 1 · 2016-12-20T21:00:49

#5.95# square units

#A_triangle = 1/2ab sin C#

the angle to take as #C# is the angle sandwiched between the #2# given sides.

angle sandwiched between A and B = #pi -( 5pi)/8 - pi/12#

#=(24pi)/24 - (15pi)/24 - (2pi)/24#

#=(7pi)/24#

#A_triangle = (3*5)/2 * sin((7pi)/24)#

#= 7.5sin((7pi)/24)#

#=5.95# square units

(NB: when using #pi# as a measurement of angles, use the #Rad# setting on your calculator)