A triangle has sides A, B, and C. Sides A and B are of lengths 22 and 55, respectively, and the angle between A and B is pi/4π4. What is the length of side C?

1 Answer
Sep 27, 2016

:. C=~~3.855.

Explanation:

We use the Cosine-Rule for DeltaABC, which states,

C^2=A^2+B^2-2ABcos(/_(A,B)),

where, by "/_(A,B), we mean the angle btwn. sides A & B..

:. C^2=2^2+5^2-2*2*5cos(pi/4)

=29-20(1/sqrt2)=29-10sqrt2

~~29-10(1.414)=29-14.14=14.86

:. C~~3.855