Question

To travel from Pottstown to Cogsville, a man drives his car 85 miles due east on one road, and then 15 miles due north on another road. Describe the path that a bird could fly in a straight line from Pottstown to Cogsville. What angle does the line make with the two roads that the man used? Express your answers to the nearest tenth of a degree.

The bird's path forms an angle of
what ° with the first (driving east) road and an angle of
what ° with the second (driving north) road.

Answer 1

Place Pottstown at (0,0) and Cogsville at (85,15). The bird flies along the straight line from (0,0) to (85,15).

Angle with the east road: θ = arctan(15/85) ≈ arctan(0.1764706) ≈ 10.0° (north of east).

Angle with the north road: 90° − θ ≈ 80.0°.

So the angles are 10.0° with the east road and 80.0° with the north road.