Chapter 11.3, Problem 43E

In Exercises 37 to 43, angle measures should be given to the nearest degree; distance should be given to the nearest tenth of a unit.

From atop a $200$-ft lookout tower, a fire is spotted due north through an angle of depression of ${12}^{\circ }.$ Firefighters located $1000$ ft due east of the tower must work their way through heavy foliage to the fire. By their compasses, through what angle (measured from the north toward the west) must the firefighters travel?