villagas A,B,C,D, are such that B is 4km due east of A, C is 3km due of south of B and D is 4km S 50 degree W from C. Calculate the distance and bearing of A from D.

First, draw a picture.

Second, calculate the east-west component of each of the three "steps" from A to B, B to C, and C to D. Use positive values for eastward direction and negative for westward. Add them up - this gives the total east-west distance from A to D.

Do the same for the north-south components of each step, and add them up.

Now that you have the total east-west movement from A to D and the total north-south movement as well, use Pythagoris to find the total distance from A to D. The bearing from A to D can be determined using the arctangent of the ratio of the east-west and north-south distances.