How do you solve a triangle if you are given a=2.5, b=10.2, c=9?

1 Answer
Alan P.
Jul 8, 2015

/_A = 0.229406 radians
/_B = 1.953156 radians
/_C = 0.959031 radians

Explanation:

For a triangle with
color(white)("XXXX")side a opposite angle A
color(white)("XXXX")side b opposite angle B
color(white)("XXXX")side c opposite angle C
The Law of Cosines says:
color(white)("XXXX")c^2 = a^2+b^2-2abcos(C)
or
color(white)("XXXX")cos(C) = (a^2+b^2-c^2)/(2ab)
color(white)("XXXX")color(white)("XXXX")(and similarly for A and B)

So
color(white)("XXXX")cos(C) = (2.5^2+10.2^2-9^2)/(2(2.5)(10.2))

color(white)("XXXX")color(white)("XXXX")=0.574314

C = "arccos"(cos(C))
color(white)("XXXX")C = "arccos"(0.574314)
color(white)("XXXX")color(white)("XXXX")=0.959031 radians
color(white)("XXXX")color(white)("XXXX")(using a calculator)

Similar calculations can be made for angles A and B

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