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From a ship, two lighthouses can be seen bearing N 40 degrees E. After the ship sails at 15 knots on a course of 135 degrees for an hour and 20 mins, the two lighthouses now has a bearing of 10 degrees and 345 degrees.
a) Find the distance of the ship from the latter position to the farther lighthouse?
b) Find the distance between the two lighthouses? .... thank you in advance.

• math- help needed badly -

The ship travels 20 miles in the time given.

If we label the points S for ship (current position), N and F for Near and Far lighthouses, then if we call the original position O,

In triangle SNF,
S=25°
N=125°
F=30°

In triangle ONS,
n = 20
N=55°
O=95°
so,
NS/sin95° = 20/sin55°

We want SF and NF
Now you can use the law of sines in NSF to find the other two sides.

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