A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 5, respectively. The angle between A and C is #(5pi)/24# and the angle between B and C is # (pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-01-26T10:51:29

The area of the triangle is #15.16(2dp) sq.unit#

The angle between sides A and C is #/_b=(5pi)/24 =5*180/24=37.5^0#

The angle between sides B and C is #/_a=pi/8 =180/8=22.5^0#

The angle between sides A and B is #/_c=180 - (37.5+22.5)=120^0#

So we have sides #A=7 ; B=5 # and their included angle #/_c=120^0#

The area of the triangle is #A_t= (A*B*sinc)/2=(7*5*sin120)/2=15.16(2dp) sq.unit# [Ans]