Question

Towers A and B are on the east-west line 125 m apart. Jojo, on the north of that line finds that the direction of towers A and B are N 39deg27mins E and N 50deg33mins W, respectively. How far is Jojo from each tower?

Answer 1

I cannot make any sense of your description.
Jojo would have to be on the south side of line AB
Check it please

Answer 2

Assuming that north was a typo, leaving Jojo on the south side of AB,

Let Jojo be h mi S of the line AB.

h tan 50°33' + h tan 39°27' = 125
1.215h + 0.823h = 125
h = 125/2.038 = 61.335 mi

Now, letting b be the distance from B, and a that from A,

b = h/cos 50°33' = 61.335/0.635 = 96.59 mi
a = h/cos 39°27' = 61.335/0.772 = 79.45 mi