A boat travels 6.3km due North and then turns 17 degrees towards the west and travels a further 7.2 km. How far is it from its initial position?

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Answer 1 · 2018-01-18T11:19:07

The boat is #13.35# km. away from its initial position.

Let the boat starts from point #A# , after travelling #6.3# km due

north reaches point #B# and then after travelling #7.2# km turns

#17^0# west and reaches point #C# . In triangle #Delta ABC ,#

#AB=6.3 , BC=7.2# and their included angle

# /_B=180-17=163^0; AC=?# Applying cosine law we find

#AC=sqrt(AB^2+BC^2-2*AB*BC*cos B)#

#=sqrt(6.3^2+7.2^2-2*6.3*7.2*cos163) ~~13.35# km.

The boat is #13.35# km. away from its initial position. [Ans]