Triangles - sin, cos etc.

Question

I know this is a quite simple question for most of you out there.

However it has been a little troubling for me, and would like to get a little help if possible.

I have a triangle $ABC$ where I know that

$C = 29^\circ$ $a = 5,2$ and the area of the triangle is $T = 8,4$

What I have to find out is $|AC|$. For me this doesn't seem possible unless I start splitting up the triangle, and work from there. Although I'm not sure if my teacher allows that, and therefore would like to know if it at all is possible?

If that should be the case, then how would I go by figuring it out? Anything not using $2$nd degree equations, $\sin$ relations or $\cos$ relations for figuring it out is not needed, (means that I have not yet been taught to use anything but those 3 to solve the problem)

If a triangle to be included is needed, I'd be happy to provide it.

Sorry for the long text, thanks.

Answer 1

This can be solved using the Sine rule.

The area of the triangle can be expressed as, $$Area=\frac12 ab\sin C$$ where $a,b$ are the lengths of the sides opposite vertices $A,B$ respectively.

Here, you have, $$Area=8.4$$ $$a=5.2$$ $$C=29°$$ Using these, you can find $b$, which is the length of the side $AC$.

Answer 2

Use the fact the area of the triangle is $$\frac {1}{2}AC.BC.\sin C$$ you have been given that BC = 5.2, and you also have the area and the angle too, so..