A monument near a dock is 12 miles east of a ship. After the ship has sailed 7 miles, the monument bears North 62 degrees East. In what direction is the ship sailing?

Answer 1

Draw a picture....

If the monument appears north of the ship, then the ship has travelled south. (with an unknown east or west component)

First, draw a right triangle with one leg due east, length 12 miles, and the other leg due south. The given bearing of the monument (62 degrees) is along the hypotenuse of this triangle. In the new position, the ship must be on the line defined by this hypotenuse.

The "south leg" of the triangle 12/tan62 = 6.38 miles. This means the ship has either travelled west of south or approximately southeast. To see the two possibilities, draw an arc, centered at the original position, with a radius of 7 miles. Graphically, it appears that the ship travelled about 20 degrees west of south, OR about 60 degrees east of south.

Again--draw a picture and use trig formulas to find the exact angles.