Question

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?

Answer 1

`abs(C)~~6.083` sq.units

Explanation:

Consider the image below:

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`