Thread: trig word problem, bearings

This is the problem: A ship is sailing due north. At a certain point the bearing of a lighthouse is N 38 E and the distance is 13.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.4 . How far did the ship travel between the two observations of the lighthouse. distance=?
Here is what I did: at A the ship tskes a bearing of the lighthouse at C and finds angle A=38 and b=AC=13.5 miles. Later at point B, they find that angle B=59.4. So, angleC= 180-38-59.4=82.6. Next we find c, I used the law of sines, 13.5sin82.6/sin59.4= 15.6 miles.

I checked and my answer is wrong, so could someone please show me what I did wrong.
Thank you!
Keith Stevens

Originally Posted by kcsteven

This is the problem: A ship is sailing due north. At a certain point the bearing of a lighthouse is N 38 E and the distance is 13.5. After a while, the captain notices that the bearing of the lighthouse is now S 59.4 . How far did the ship travel between the two observations of the lighthouse. distance=?
Here is what I did: at A the ship tskes a bearing of the lighthouse at C and finds angle A=38 and b=AC=13.5 miles. Later at point B, they find that angle B=59.4. So, angleC= 180-38-59.4=82.6. Next we find c, I used the law of sines, 13.5sin82.6/sin59.4= 15.6 miles.

I checked and my answer is wrong, so could someone please show me what I did wrong.
Thank you!
Keith Stevens

Looks OK to me: 15.553511. Checks out on a scale diagram to the limits
of accuracy of the drawing.

RonL

Hello, Keith!

I see absolutely nothing wrong with your work . . .

A ship is sailing due north. .At a certain point
the bearing of a lighthouse is and the distance is miles.
After a while, the captain notices that the bearing of the lighthouse is now
How far did the ship travel between the two observations of the lighthouse?

Here is what I did:
At the ship takes a bearing of the lighthouse at and finds miles.

Later at point , they find that
So: .

Next we find ,
I used the Law of Sines: . miles.

I checked and my answer is wrong.

Either: [1] You copied one of the numbers incorrectly
. . .or: [2] your book is dead wrong.