Point A is where you're standing. Point B is the first tower. Point C is the second tower.
First let's find angle B using the law of cosines.
24202 = 50502 + 60002 - (2)(5050)(6000)(cosB)
5856400 = 61502500 - 60600000cosB
-55646100/-60600000 = cosB
0.91825 ≈ cosB
B ≈ 23.328°
So the angle that I think the problem is asking for is approximately 23.3°.
Next we can find x.
cosB=x/5050
0.91825 ≈ x/5050
x ≈ 4637.163
So the position east of the tower is approximately 4,637.2 feet
Next we can find y.
sinB=y/5050
0.39599 ≈ y/5050
y ≈ 1999.771
So the position north of the tower is approximately 1,999.8 feet.