Precalc/Trigonometry Math Question

<p>Hi everyone. I'm really stuck on this problem and have no idea how to get the answer. Here it is:</p>

<p>"Two fire towers A and B are 30 km apart. The bearing from A to B is N 65 E. A fire is spotted by a ranger in each tower and its bearings from A to B are N28E and N16.5W respectively. Find the distance of the fire from each tower."</p>

<p>A figure is provided with towers A and B 30 km apart and forming a triangle with the burning house. The bearings of 28 degrees, 65 degrees, and 16.5 degrees are shown in their correct places. Can anyone help??</p>

<p>Thanks. I'm usually a really strong precalc student but these word problems are really stumping me. :)</p>

<p>Sorry I can't help but these were the only things I didn't get in pre-calc. No one understood them/they even confused the teacher a bit so he just made them extra credit in which everyone just guessed. So yeah, they're hard and I would help if I remembered.</p>

<p>Thanks Logistics. You really post everywhere, lol. Oh well. I think I'm going to keep staring at the problem but I don't seem to be getting anywhere. Worse yet, I still didn't get another one and the 2nd one doesn't even have a picture to look at. Oh well.</p>

<p>Do you understand bearing? I think that's what really gets me. :)</p>

<p>No that's what was the hard things in pre-calc...bearing. Everything else was a cakewalk. He told us since he had trouble with it, we would so he made them only bonus on his tests. Bearings...you could probably google a quick tutorial.</p>

<p>i believe you can use law of sines or law or cosines for this...</p>

<p>might have to actually see the problem...</p>

<p>use law of sines</p>

<p>a/sinA=b/sinB=c/sinC</p>

<p>where the lower case letter is a side, and the respective upper case letter is the angle opposite that side. Plug in and solve and you should get the right answer.</p>

<p>I would need to see the diagram, or a better description to tell you how to do this specific one.</p>

<p>A side note: what the heck are "bearings"?</p>

<p>^^^ How can you possibly know how to do it without knowing what bearings are??</p>

<p>Lol>..........</p>

<p>Yeah. It's in our section about Law of Sines so I know that applies, but I really don't understand how to find out the measures of the angles or sides so I have enough info to use Law of Sines. Oh well...thanks for the help everyone. I guess I'll just ask my teacher tomorrow. :)</p>

<p>I think that is how to answer the question because of how he described the diagram. If bearings are what I got the impression they are, or if they just are the angles of the triangle, then what I said applies.</p>

<p>If not... dunno.</p>

<p>First of all, I am assuming we are talking about plane rather than spherical geometry.</p>

<p>Lets call A the location of tower A, B the location of tower B and C the location of the fire. If A to B is 65 degrees east of north and A to C is 28 degrees east of north, then angle BAC is 37 degrees. Now make another point which we will call D, directly east of A and directly south of B. Angle DAB is 90 - 65 or 25 degrees, angle ADB is 90 degrees, so angle DBA must be 65 degrees. Now draw a line from D due north, through and past point B. Since the direction from B to C is 16.5 degrees west of north, the angle CBA must be 180 - 16.5 - 65 or 98.5 degrees. Therefore angle BCA must be 180 - 98.5 - 37 or 44.5 degrees. You now have a triangle with three known angles and one known side. Use the law of sines to get the other sides.</p>

<p>Aww...my triangle drawing got messed up! Anyway, I agree with bassdad.</p>

<p>Everyone in my class had some difficulty with these types of problems, but here is a suggestion: get on the internet and look for some precal help sites. That is the best I can do-I am studying for AP Chem test on Chemical Kinetics-or something like that.</p>

<p>OMG! I had the exact same homework problem! Do you use university of texas homework service?</p>

<p>seriously, what are bearings in this context? also, for future reference, try <a href="http://physicsforums.com%5B/url%5D"&gt;http://physicsforums.com&lt;/a> . great website for physics and math homework help.</p>

<p>i love these questions...these are the easiest ones in pre-calc...i did exactly what bassdad...keep in mind i never saw his post until later today...gj bassdad, that was good</p>

<p>A bearing is simply an angle between a reference direction (usually due north) and some other object, as observed from a given point. In this case, we are told that the bearing of tower B from tower A is N65E, meaning that If I am sitting in tower A, then tower B would be in a direction 65 degrees east of due north. Likewise the direction toward the fire from tower A is 28 degrees east of north and the direction toward the fire from tower B is 16.5 degrees west of due north.</p>

<p>When observing a fire from either tower alone, it would be difficult to estimate the distance to the fire but very easy to measure the direction. In order to tell the firefighters exactly where to go, you need bearings from two towers. If you draw the towers on a map and draw a line along the bearing frome each one to the fire, the location of the fire is at the intersection of the lines.</p>

<p>I love how BestMiler just had to say they were the easiest to contradict me. I love it. I guess these were much easier than questions merely involving a pole and a shadow. Now those were easy. Bearings are basically the degrees and direction traveled. Usually its not so bad when they give you a pic. When you have to make your own pic it gets confusing. We did this before we learned law of sines so I don't know how we were supposed to do it. Usually you got these really odd /complex pictures with like trapezoids and crap in there.</p>

<p>I swear, i never meant to contradict you...i always found them easy, but im not going to lie, they were sometimes paing and annoying....and also i was learnign them in IB Math, where there were more harder topics, so i guess i found the topic on bearing a lot easier than the other ones</p>

<p>This was an example of one of the easier ones from my class last year. I think it might be similar but not sure:</p>

<p>A ship leaves port and travels due east 15 nautical miles, the changes course to N 20 deg. W and travels 40 more miles, find the bearing to pot of departure.</p>

<p>Anyone know how you would do that for ref purposes?</p>