A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 8, 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?

1 Answer
SCooke
Jun 15, 2017

33

Explanation:

#Degrees = (180/pi)*radians#
(I just like working in degrees better)

Law of Cosines equation is #c^2 = a^2 + b^2 – 2*a*b*cos(gamma)#.

The angle #gamma# needed is #180 – (37.5 + 67.5)# = #180 - 105# = #75#

#c^2 = 10^2 + 8^2 – 2*10*8*cos(75)#.
#c^2 = 100 + 64 – 160*(0.259)#.
#c^2 = 122.6# : #c = 11#
Then using these values we can now find the height #h# for the triangle and solve for the area. #sin(37.5) = h/10#
#h = sin(37.5) * 10# ; #h = 6#
#A = (1/2)*b*h# ; #A = (1/2)*11*6 = 33#

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