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Kisachek [45]
3 years ago
15

The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further from the lighthouse. The new bearing is 25°

E. What is the distance between the lighthouse and ship at the new location?
Mathematics
1 answer:
djverab [1.8K]3 years ago
3 0

Answer:

The distance between the ship at N 25°E and the lighthouse would be 7.26 miles.

Step-by-step explanation:

The question is incomplete. The complete question should be

The bearing of a lighthouse from a ship is N 37° E. The ship sails 2.5 miles further towards the south. The new bearing is N 25°E. What is the distance between the lighthouse and the ship at the new location?

Given the initial bearing of a lighthouse from the ship is N 37° E. So, \angle ABN is 37°. We can see from the diagram that \angle ABC would be 180-37= 143°.

Also, the new bearing is N 25°E. So, \angle BCA would be 25°.

Now we can find \angle BAC. As the sum of the internal angle of a triangle is 180°.

\angle ABC+\angle BCA+\angle BAC=180\\143+25+\angle BAC=180\\\angle BAC=180-143-25\\\angle BAC=12

Also, it was given that ship sails 2.5 miles from N 37° E to N 25°E. We can see from the diagram that this distance would be our BC.

And let us assume the distance between the lighthouse and the ship at N 25°E is AC=x

We can apply the sine rule now.

\frac{x}{sin(143)}=\frac{2.5}{sin(12)}\\ \\x=\frac{2.5}{sin(12)}\times sin(143)\\\\x=\frac{2.5}{0.207}\times 0.601\\ \\x=7.26\ miles

So, the distance between the ship at N 25°E and the lighthouse is 7.26 miles.

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