A ship is sailing due north. At a certain​ point, the bearing of a lighthouse 6.16.1 km away is N36.236.2degrees°E.Later​ on, the captain notices that the bearing of the lighthouse has become S 33.2 degrees E.How far did the ship travel between the two observations of the​ lighthouse?

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Asked Nov 18, 2019
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A ship is sailing due north. At a certain​ point, the bearing of a lighthouse 6.16.1 km away is N36.236.2degrees°E.

Later​ on, the captain notices that the bearing of the lighthouse has become S 33.2 degrees E.

How far did the ship travel between the two observations of the​ lighthouse?

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Expert Answer

Step 1

Given,

           A ship is sailing due north. At a certain​ point, the bearing of a lighthouse 6.1 km away is N 36.2 degrees° E. Later​ on, the captain notices that the bearing of the lighthouse has become S 33.2 degrees E.

The above situation is dawn below.

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A 1st Position 36.2 C Light House у х 33.2 6.1 km B Later on 2nd position

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Step 2

Now, by angle sum property of...

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. 36.2°33.2° y = 180° y110.6 Now, applying laws of Sines, we get sin 36.2 sin 110.6° 6.1 6.1 sin 110.6° x sin 36.2 x = 9.6679 x 9.7 km

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Trigonometry

Trigonometric Ratios