Question

Bearings Problem Solving Question:

Answer 1

9514 1404 393

Answer:

  a) 123.4°

  b) 3.3 km

Step-by-step explanation:

In (N, E) coordinates, Boat 1 is located relative to the lighthouse at ...

  2(cos(60°), sin(60°)) = (1.0, 1.732) . . . . . km

Boat 2 is located at ...

  3(cost(340°), sin(340°)) = (2.819, -1.026) . . . . . km

So, relative to Boat 2, Boat 1 is located at ...

  (1, 1.732) -(2.819, -1.026) = (-1.819, 2.758) . . . . . km

This is at a bearing of ...

  arctan(2.758/-1.819) = 123.4°

and a distance of ...

  √(1.819² +2.758²) ≈ 3.304 . . . . . km

a) Boat 2 would need to travel on a bearing of 123.4°.

b) Boat 2 would need to travel 3.3 km.

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Additional comment

We use (North, East) coordinates so we don't have to do the mental gyrations necessary to translate to and from (E, N) coordinates. The latter would correctly orient a map relative to the X-Y Cartesian plane. The former are equivalent to flipping the map over and looking at it from the back side. This is a "rigid transformation", so angles and distances remain unchanged.