A triangle has sides A, B, and C. Sides A and B have lengths of 6 and 5, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-11-18T11:03:06

Area of the triangle is #14.49# sq.unit.

Angle between Sides # A and C# is

# /_b= (5pi)/24=(5*180)/24=37.5^0#

Angle between Sides # B and C# is

# /_a= (3pi)/8=(3*180)/8=67.5^0 :.#

Angle between Sides # A and B# is

# /_c= 180-(37.5+67.5)=75^0#

Now we know sides #A=6 , B=5# and their included angle

#/_c = 75^0#. Area of the triangle is #A_t=(A*B*sinc)/2#

#:.A_t=(6*5*sin75)/2 ~~ 14.49# sq.unit

Area of the triangle is #14.49# sq.unit [Ans]