Question

Two boats, A and B, are approaching a port. The distance between the boats is 12 miles. The bearings of the port with respect to boat A and boat B are N 60° W and N 35° E respectively. How far is boat A from the port?

Answer 1

find the port angle

Answer 2

180 - 60 - 35 = 95 degrees

Answer 3

now use law of sines to find the length of the side from A to the port

Answer 4

12/sin(95) = 12.045

Answer 5

x/sin(35) = 12.045

Answer 6

solving for x:
we get x=6.9

Answer 7

therefore the length is 6.9 miles

Answer 8

11.02 miles?
9.87 miles?
8.23 miles?
4.54 miles?
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