Date: 06/11/2000 at 07:17:59 From: Rachel Crane Subject: Bearings I have my end of year exams coming up this week. One of the questions on the paper will be about bearings, and I don't understand a bit of it: From a ship, A, the bearing of an oil tanker, T, is 300 degrees. From a second ship, B, which is 1000 m due west of A, the bearing of the oil tanker is 060 degrees. Explain why the oil tanker is the same distance from A as it is from B. (I also have to draw a rough sketch.) Could you help me, please? Thank you so much, Rachel Crane
Date: 06/14/2000 at 08:30:18 From: Doctor Rick Subject: Re: Bearings Hi, Rachel, A bearing is a direction, measured as an angle going clockwise from north. North is 0 degrees, east is 90 degrees, south is 180 degrees, and west is 270 degrees. In pure math the convention is to measure directions going counterclockwise from "east" (the positive x axis), but in practical fields like surveying or navigation, bearings are used. Don't ask me why there are two different systems; I guess the people who invented them just never talked with each other. You can use bearings to draw the geometrical figures requested in your problem, and then use more familiar geometry to answer the question. Let's look at the problem: >A) From a ship, A, the bearing of an oil tanker, T, is 300 degrees. >From a second ship, B, which is 1000 m due west of A, the bearing of >the oil tanker is 060 degrees. Explain why the oil tanker is the same >distance from A as it is from B. (I also have to draw a rough >sketch.) Draw a point A. Then draw a ray from A at a bearing of 300 degrees. Going 300 degrees clockwise from north (up, in your drawing) is the same as going 60 degrees counterclockwise, because 300 + 60 = 360 degrees, a full circle. We don't know where P is yet, so I'll label a point on the ray Q just so we can identify the ray. It will look like this: Q _ North |\ ^ \ | \ 60| \ | *A Draw a line from A to B. It goes west (to the right) from A. Make it any length but label it 1000 m. Q _ N |\ ^ \ | \ 60| 30 \ | B*------------*A What is the angle between AQ and AB? Since angle NAB is a right angle, angle NAQ + angle QAB = 90 degrees. Therefore angle QAB = 30 degrees. We have one more ray to draw, the ray BP. Its bearing is 060, that is, 60 degrees clockwise from north. I'll let you draw it because my figure would get too complicated. Do the same thing I did above: draw a line north from B, and mark off an angle of 60 degrees on the right side of that line. What is the angle between the ray you have drawn and BA? Mark P on the figure, at the intersection of AQ and the new ray. Now you have enough information to answer the question. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
Date: 06/15/2000 at 11:38:43 From: Rachel Crane Subject: Re: Bearings Thanks for your message, Dr. Rick. It has helped me a lot. All I need now is some good luck for tomorrow's math test! Cheers, Rachel Crane
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