A triangle has sides A, B, and C. Sides A and B are of lengths #4# and #12#, respectively, and the angle between A and B is #pi/3#. What is the length of side C?

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Answer 1 · 2018-02-05T07:59:02

See explanation.

If you have 2 sides of a triangle given and the angle between them, you can use the Cosine Theorem to calculate the remaining side:

#C^2=A^2+B^2-2ABcosc#

where #c# is the angle opposite to side #C# (i.e. angle between #A# and #B#)

If we apply the given data we have:

#C^2=4^2+12^2-2*4*12*cos(pi/3)#

#C^2=16+144-96*1/2#

#C^2=160-48=112#

#C=sqrt(112)=4sqrt(7)#