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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