Solve Cartesian and Polar Coordinates, Distance, and Direction Problems"

[graffz]

1) Two points in the xy plane have Cartesian coordinates (1.00, -4.00) m and (-5.00, 5.00) m. Determine their polar coordinates @ (-5.00, 5.00)
r = ?
θ = ?

2) A plane flies from base camp to Lake A, 290 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 230 km 30.0° west of north from Lake A. Graphically determine the distance and direction from Lake B to the base camp.
Distance = ?
Direction = ?

3) Given the vectors = 5.00 + 8.00 and = 3.00 - 2.00.
vector D
r =
θ =


I have absolutely no clue how to solve these, or where to begin. I don't have my book yet since it has not been delivered, and I don't mean to be a pest, but I really need help. Thank you!

 

[graffz]

AND ANOTHER ONE, PLEASE.

An air-traffic controller observes two aircraft on his radar screen. The first is at altitude 850 m, horizontal distance 19.8 km, and 25.5° south of west. The second aircraft is at altitude 1000 m, horizontal distance 18.0 km, and 19.0° south of west. What is the distance between the two aircraft? (Place the x-axis west, the y-axis south, and the z axis vertical.)