# A ship leaves port on a bearing of 28 degrees and travels 8.2 km.  The ship then turns due east and travels 4.3 km.  How far is the ship from the port, and what is its bearing from the port?

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A ship leaves port on a bearing of 28 degrees and travels 8.2 km.  The ship then turns due east and travels 4.3 km.  How far is the ship from the port, and what is its bearing from the port?

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Step 1

To find distance between the ship from port and its bearing from port.

Let B be the port and A is the point at which ship reaches after travelling  28°  and 8.2 km. from the port.

C is the point at which ship turns due east and reaches after travelling 4.3 km.

Use the above information to draw the explanatory diagram as below:

Step 2

From Figure, it is observed that ANB is the right angle triangle.

∠NAB  =   ∠ANB − ∠NBA

=    90° − 28°

=    62°

From Figure, it is observed that NAC  is the straight line.

BAC  =   180°−  ∠NAB

=    180° − 62°

=    118°

Step 3

Use the cosine formula to find the distance b...

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