SOLUTION: A boat heads out to sea from a port that sits along a straight shoreline. The boat heads in a direction that makes a 70 degree angle with the shoreline. After sailing for 3 miles,

Question 143826: A boat heads out to sea from a port that sits along a straight shoreline. The boat heads in a direction that makes a 70 degree angle with the shoreline. After sailing for 3 miles, the skipper looks back at the shore and sees his house. The house, like the port, also sits on the shore. The lines of sight to the port and to his home make an 80 degree angle. How far is the skipper's home from the port? Round your answer to the nearest tenth of a mile.
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
It's a good idea to draw a diagram of the situation if you can.
I don't know how to do diagrams on this site, but, on paper, you would end up with a triangle in which the shoreline between the port and the skipper's home is represented by the base of the triangle whose length (b) would then represent the distance from the port to the skipper's home.
The left leg of the triangle makes a 70-degree angle with the base (shoreline) and it is 3 miles in length.
The right leg of the triangle makes an 80-degree with the 3-mile leg and connects to the skipper's home.
So, we know the three angles of the triangle are 70 degrees, 80 degrees, and 30 degrees with the two base angles being 70 degrees and 30 degrees.
Now you can use the law of sines to find the distance, b, from the port to the skipper's home.
Law of sines:
In your diagram, let's label the 70-degrees angle as A, so the side opposite this angle is labeled a.
The 80-degree angle is labeled B, so the base of the triangle is b and this what we are trying to find.
The 30-degree angle is labeled C and the 3-mile leg would be c.
So, we can write:

Multiply both sides by sin80.
You can do this with your calculator.
miles.

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