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A ship at position (1, 0) on a nautical chart (with north in the positive y direction) sights a rock at position (4, 7). What is the vector joining the ship to the rock?

What angle θ does this vector make with due north? (This is called the bearing of the rock from the ship. Round your answer to two decimal places.)

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sqdancefan

Answer:

  • (3, 7)
  • 23.20°

Step-by-step explanation:

The vector in component form is the difference of the coordinates of its end points:

  rock - ship = (4, 7) - (1, 0) = (3, 7) . . . . vector from ship to rock

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The angle from North can be found using the tangent relation:

  tan(bearing) = (east distance)/(north distance) = 3/7

  bearing = arctan(3/7) ≈ 23.1986°

The bearing of the rock is 23.20°.

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