A triangle has sides A, B, and C. Sides A and B are of lengths 7 and 4, respectively, and the angle between A and B is pi/3. What is the length of side C?

1 Answer
Alan P.
Nov 7, 2016

abs(C)~~6.083 sq.units

Explanation:

Consider the image below:
enter image source here
Remember that
color(white)("XXX")sin(pi/3)=sqrt(3)/2color(white)("XX")andcolor(white)("XX")cos(pi/3)=1/2

Based on this we have:
color(white)("XXX")h=7sin(pi/3) ~~6.0621778265

color(white)("XXX")x=7cos(pi/3)=3.5

color(white)("XXX")k=4-x=0.5

color(white)("XXX")abs(C)=sqrt(h^2+k^2)~~6.0827625303

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