two lighthouses are situated such that B is 7 km directly east of lighthouse A. A ship at point P observes that A is due north and that the bearing of B is 46°10'. How far is the ship from A and B ?

Answer 1

According to my sketch:
tan46°10' = 7/AP
AP = 7/ tan46°10' = ....

sin46°10' = 7/BP
BP = 7/sin46°10' = ....

Answer 2

how do you sketch this kind of problem?, that's the reason why i'm having trouble with this ..

Answer 3

first thing, of course, is to draw line AB. B is east of A, so it's horizontal.

A is due north of P, so draw a line south from A and put P somewhere on it.

You can estimate angles, at least to some degree :-) so make PB at about 45 degrees.