A ranger at forest station A( located at latitude N47 and longitude W116 30') sights smoke from a fire in the direction of S35 36'W. At the same time a ranger at forest station B(located at latitude N48 and longitude W117 45') sights the same fire in the direction of S54 18'E. Locate the fire's longitude and latitude to the nearest minute and it's distance from each of the forest station.

Question

I got the distance from station A and B as 90.409 miles I just don't know where to go next.

Answer 1

which kind of trig are we using?

Answer 2

earth flat at this range :)

Answer 3

In my sketch the position of A and B are as follows:
B is to the "left" of A and "up" from A
the rise is 1° and the run is 1.25°
So the line AB makes an angle of 38.66° with the horizontal.
I then sketched in the position of the fire F and got triangle ABF.
All possible angles at A and B can be found, thus angle F is also known.
So you know all the angles

You said you found AB = 90.409 miles.

But 1° along a great circle = 60 nautical miles
so AB in degrees = √(60^2 + 75^2) = 96.05 nautical miles which is appr 110.55 statute miles.

So I don't see how you got 90.4 miles.
Once that is resolved, use the Sine Law to find the distances between the fire and the stations.

Just a lot of messy conversions to get the coordinates back.

Answer 4

@Steve sine, cosine, and tangent also the law of sines and cosines

Answer 5

@Reiny idk my teacher just told me to use movable-typedotcom to find the distance between the two points