Hello so this problem came up while I was studying trig. and I seem a bit stuck:
Calculate the area of a triangular field, knowing that two of its sides measure $80$ m and $130$ m and between them is an angle of $70°$.
To solve this problem I drew altitude and
So with this diagram I used the $Z$ side as common to find two equations using $\sin$: $$\sin x= Z/80$$ $$\sin y=Z/130$$
which gives
$$Z=\sin x*80$$ $$Z=\sin y*130$$
and also $70+x+y=180$, so $x+y=110$.
So now I have two equations with two unknowns but I don't know how to solve them because the unknowns are in $\sin$.
Note: I have not yet learned about laws of $\sin$, $\cos$... So is there a way to solve this question without using such formulas??