How do I do this problem?

2015-11-24 1:24 am
A ship is 50 miles east and 35 miles south of port. The captain wants to sail directly to port. What bearing should be taken? (Round your answer to two decimal places.)

回答 (2)

2015-11-24 2:32 am
A latitudinal ("horizontal") line in the west-to-east direction forms one side of
a right triangle. That line is 50 miles long. A longitudinal ("vertical") line in the
north-to-south direction and 35 miles long forms the second side of the right
triangle. The sip is currently located at the end of the longitudinal line. The
straight-line course to port that the captain wishes to take forms the third side
of the right triangle and is the hypotenuse of the right triangle.

A = latitudinal line = 50 miles
B = longitudinal line = 35 miles
H = hypotenuse; intended course straight to port
α = angle between line B and line H = to be determined

tan α = A/B = 50/35 = 1.428571429
α = arctan (1.428571) = 55.0079798 °
α = 55.01 ° ANSWER

β = angle as measured CCW from the positive x-axis = to be determined
β = 90.00° + α = 90.00° + 55.01° = 145.00798 °
β = 145.01 ° ANSWER

ε = complementary angle to α = to be determined
ε = 90.00° - α = 90.00° - 55.01° = 34.9920202 °
ε = 34.99 °

θ = angle as measured CW from NORTH = 0° (compass bearing) = to be determined
θ = 270.00° + ε = 270.00° + 34.99° = 304.99202 °
θ = 304.99 ° ANSWER
2015-11-24 1:27 am
True Bearing or Compass Bearing ?


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