Question

How do you find the angle C formed by the sides of length 2, 3, and 7?

Answer 1

Not such triangle exists (you can't have a triangle where one side is more that the sum of the lengths of the other two sides).

However, to demonstrate the process:
(and noting that you could get 3 different answers depending upon which side you decide angle C is opposite.)

For demonstration purposes, I will assume the sides are
`a=2, b=3, " and " c=7`
with angle C opposite side `c`

The Law of Cosines:
`c^2=a^2+b^2-2ab*cos(C)`
can be rearranged as
`cos(C) = (a^2+b^2-c^2)/(2ab)`

`C=arccos(cos(C)) = arccos((a^2+b^2-c^2)/(2ab))`

for the supplied values
`C = arccos( (4+9-49)/12)`

beyond this you should be able to do the arithmetic and look up the `arccos()` value in a table or on a calculator... but as noted at the beginning it's all moot since the triangle can't exist.