A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.
A) $131 ^ { \circ } 30 ^ { \prime }$
B) $129 ^ { \circ } 27 ^ { \prime }$
C) $132 ^ { \circ } 32 ^ { \prime }$
D) $48 ^ { \circ } 30 ^ { \prime }$
E) $134 ^ { \circ } 29 ^ { \prime }$

Question

Quizplus · Accepted Answer

To find the bearing, we calculate the angle using the tangent function, where tangent of the angle = opposite/adjacent = 46/52. The arctan(46/52) gives the angle from the east-west line towards the north, which needs to be converted to a bearing. The bearing is 180 - angle because bearings are measured clockwise from the north. Calculating this gives a bearing of approximately 131.5 degrees, which is $131 ^ { \circ } 30 ^ { \prime }$.

A Plane Is 52 Miles West and 46 Miles North 131∘30′131 ^ { \circ } 30 ^ { \prime }131∘30′

A Plane Is 52 Miles West and 46 Miles North $131 ^ { \circ } 30 ^ { \prime }$