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 #(pi)/3# and the angle between B and C is # (pi)/4#. What is the area of the triangle?

1 Answer
Roella W.
Jan 19, 2016

#A~~6.54#

Explanation:

Sketch
The area of a triangle is given by #1/2*Base*height#
The height #h# in this example can be found from
#sin(pi/3) =h/A = h/3#
#h = 3sin(pi/3)#

The base #C = x +y# and #x# and #y# can also be found from trigonometric functions.
#x/A = cos(pi/3)# so #x = 3cos(pi/3)#
#y/B = cos(pi/4)# so # y = 5cos(pi/4)#

Area #A = 1/2*(3cos(pi/3)+5cos(pi/4))*3sin(pi/3)#

#A =1/2*(3*0.5 +5*0.7071)*3*0.866#
#A~~6.54#

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