How do you find the area of the triangle given C=85 degrees, a= 2, B= 19 degrees?

1 Answer
Alan P.
May 10, 2015

If #/_ B = 19^o# and #/_C = 85^o#
then
#/_A = 180^o - (/_B + /_C) = 76^o#

We can use the Law of Sines

#(2)/(sin(76^o)) = (b)/(sin(19^o)) = (c)/(sin(85^o)#

To determine the lengths:
#b=0.67107# (approx.)
#c=2.53384# (approx.)

Then use Heron's Formula for the area of the triangle
#A=sqrt(s(s-a)(s-b)(s-c))#
where #s# is half the perimeter of the triangle

In this case (assuming no arithmetic errors)
Area of the triangle# = 0.741216#

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