Two fire towers A and B are 18.5 miles apart. The bearing from A to B is 65 degrees. A fire is spotted by the ranger in each tower, and its bearings from A and B are 28 degrees and 343 degrees, respectively. Find the distance of the fire from each tower.
I don't at all understand bearings, so any help with it would be great.
Thanks!
I don't at all understand bearings, so any help with it would be great.
Thanks!
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Draw a rough diagram of the situation. Angles only need to be approximately correct. Call the position of the fire F. Include North lines AN from A and BM from B. Write on the angles which you know. These are
NAF = 28, NAB = 65, MBF = 360 - 343 = 17.
From this you should see that FAB = 65 - 28 = 37 and AFB = 28 + 17 = 45
What angle must ABF be?
You can now use the sine rule for triangles which in this case becomes
18.5/sin45 = FB/sin37 = FA/sinFBA
Can you finish from there?
EDIT. By the way, bearings should always be given as three figure numbers.
Bearing of fire from A = 028
Bearing of B from A = 065
NAF = 28, NAB = 65, MBF = 360 - 343 = 17.
From this you should see that FAB = 65 - 28 = 37 and AFB = 28 + 17 = 45
What angle must ABF be?
You can now use the sine rule for triangles which in this case becomes
18.5/sin45 = FB/sin37 = FA/sinFBA
Can you finish from there?
EDIT. By the way, bearings should always be given as three figure numbers.
Bearing of fire from A = 028
Bearing of B from A = 065