Fire sighted from two ranger stations? HELP!!!! URGENT!!!!!?

Question

A fire is sighted from two ranger stations that are 5000m apart. The angles of observation to the fire measure 52 degrees from one station and 41 degrees from the other station. Find the distance along the line of sight to the fire from the closer of the two stations?

I tried doing this problem more than 5 times but I can't seem to get the right answer

Answer 1

Draw a diagram. I visualize two points, A and B, which are 5000 m apart and a line AB. A sights a fire that is 52 degrees from AB (going counterclockwise). towards a point C. B sights the fire that is 41 degrees (going clockwise) towards a point C. C is where the two angles intersect. Since you can find angle C, you can use the law of sines to calculate the lengths of AC and BC. (hint:AC is probably closer).

Answer 2

You have to use proportions:

If two angles of the triangle are 52 & 41, then the other is 87 (180-52-41)

If you draw a triangle you would put the two bottom angles as 52 & 41 and the length between them as 5000.

That 5000 side is directly opposite the 87 degree angle.

If you do 87x = 5000, the ratio is 57.4712 per degree.

So opposite the 52 degree angle would five you the distance from the second station because it is opposite the angle. That would be 2988.5m

Opposite the 41 degree angle would give you the distance from the first station, which would be 2356.3m - This would be the closer station

Answer 3

Draw this problem out. Make a line that represents "5000 meters" across the bottom of the page. Put one ranger station at one end, the other at the other. Now draw a line at a 41 degree angle from one station, and a 52 degree angle from the other. Because you have the two angles from the big triangle, you can find the third. Now you have all angles, and the length of a side. Where they intersect, the fire, drop a line perpendicular to the base-line ( the one that is 5000 meters long between the stations). Use SohCahToa (Sine is opposite over hypotenuse, Cosine is adjacent over hypotenuse, Tangent is opposite over adjacent) and the law of sines/cosines. Don't forget that your numbers are currently in degrees, and may need to be in radians depending on how you do your calculation. Good luck!
Also check these:
http://en.wikipedia.org/wiki/Triangulation
http://en.wikibooks.org/wiki/Trigonometry
http://en.wikipedia.org/wiki/Trigonometry

Answer 4

Ok. Ill walk you through so you can show your work.
1. draw two dots (the first and secound observation posts)
2. Draw a line from one dot to the other and label that line 5000m
3. Create a third dot (the fire)
4. Draw new lines from the dots to the fire.
5. Label the measures of the angles 52 and 41.
6. Between 52 degrees and 41 degrees, 52 degrees will be closer. so basicly were trying to find the distance between the fire and the dot maked 52.
7. Draw a perpindicular line between the line called 5000m and the fire.
8. use Trig to find out the answer.

Answer 5

456