Long Trip to Berlin, but need help with trig

[SgtMal]

LAST EDITED ON Jan-15-03 AT 04:03PM (EST)[p]In the fighter campaign, a tactic I've been applying for a while is to fly over the battle line and bomb factories, refineries, and other enemy goodies. This is easy enough when these targets are close to the battle line because I can just fly/warp to a particular grid location on the battle line and fly to a "simple" angle on the compass--such as 90, 180, or 135 degrees past the battle line to a target. This has been working well, but now, I want to get a bit more ambitious.

I want to bomb Berlin. On the map with my current battle line, Berlin is about a dozen grid marks away, so if my compass reading is even 5 degrees off, I may miss the city. That is particularly important to avoid for a mission like this because I'm fairly certain I can't warp on a mission like this, so I will have to fly "real-time." I figure it could take about an hour. It'd be a drag to fly for an hour and have nothing to see.

On to my question, I need to figure out what compass heading to follow, and I think the answer comes from trigonometry. Using the grid in the map, I know how many "grid-units" out and up (or maybe down) I need to go to get to Berlin. This forms a right triangle. That is, I have the x & y of a triangle, which trigonometry refers as opposite & adjoining sides for the angle I need. I could even get more precise by using half-grid units, since Berlin is located between a grid intersection. But, my days in a trig classroom were many moons ago, and I've spent a couple of hours looking on the Web for the formula to get an angle based on the length of x & y -- with no luck.

Does anybody know the trig formula to figure out an angle based on an adjoining and opposite leg of a triangle? For example, if Berlin is 12 grids away and 5 down, what's the angle I need?

I've asked a few folks this question in person. Some have told me about the Pathagarian Theorum and about how sin, cos, & tan are calculated. These items don't directly answer my question because I need the formula for finding an angle when I know the joining and opposite angles of triangle. That answer will get me to Berlin.

I also know that I could use the longitude and latitude that is available in the game, but I'd rather do this in a historically-accurate way, with a compass.

[CoyotePete]

Try the easy way... fly directly east for x miles until Berlin should be directly 135 degrees from your current position, then fly in that direction.

[bushman]

Ok, i'll show u how to work it out:

The trig sign we need is Tangent.

So TanX = 5 divided by 12


I'll get my calculator:

The answer is approx 22 degrees


So we add that to 90, and get 112 degrees, which the bearing.



Hope that helps

[SgtMal]

Thanks, that's just what I was looking for!

I was able to replicate your math, with 1 exception. I think you have a typo in your response. The trig formula that is needed is inverse tangent, instead of tangent. When I used inverse tangent, I was able to replicate your math.

After spending yet more time searching the Web for this trig formula, I finally found a simple one at:

http://cap.epsb.ca/math14_Jim/math9/strand3/3103anglestan.htm

On to a long ride to Berlin...
(and very curious how it'll affect the battle line)

[bushman]

Oh yes, sorry, reverse tangent. I always forget that, but it still works out ok, cause on my calculator, you press '2nd F' then 'Tan' to get reverse Tangent, and I just remember to press '2nd F' to get an angle.