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R J Kinloch
26th Mar 2008, 13:24
For all you navigators out there.
My daughter has a school problem as follows:
a Car drives 128 KM on a bearing of 53 degrees true and then travels 93 KM on a road bearing 138 degrees true.
A: Find the distance of the car from it's starting point.
B: Find the bearing of the starting point from the car.
Please show the working as the problem has an answer that doesn't fit the parameters.

Many thanks from a confused and tired dad!:rolleyes:

Solid Rust Twotter
26th Mar 2008, 13:52
Here ya go....

http://en.wikipedia.org/wiki/Law_of_cosines

I'm guessing it's simple geometry, rather than spherical geometry you're after.

airship
26th Mar 2008, 13:59
Please show the working as the problem has an answer that doesn't fit the parameters. Well, the 1st problem is going to be that there aren't any roads that straight or that long. Using a crow instead of a car would have been more realistic...?! :D

airborne_artist
26th Mar 2008, 14:55
I make it 164 km on a bearing of 270 (to the nearest degree)

You have to work out the dimensions of the first two triangles, which then gives you a third triangle which is the solution.

http://www.hrmconsultancy.net/pprune/trig.jpg

Never try to do things you've not practised for 30 years, while on lunch break...

UniFoxOs
26th Mar 2008, 15:04
I make it 101.7 miles

Wouldn't KM have been more use??

/Pedant mode OFF

airborne_artist
26th Mar 2008, 15:08
Wouldn't KM have been more use??

Cheers :ok:

Mariner9
26th Mar 2008, 15:12
Neat solution aa:D, and I haven't checked your maths, but:

B: Find the bearing of the starting point from the car

Gross error check required:=

corsair
26th Mar 2008, 15:13
Get her a GPS!

UniFoxOs
26th Mar 2008, 15:21
Actually, AA, your miles figure is probably nearer right. 128KM on 53 deg takes you 128 KM away from starting point, 93KM on a bearing of 138 must take you farther than the previous vector, so the answer must be more than 128KM??

UFO

airborne_artist
26th Mar 2008, 15:22
OK, so the bearing of the starting point from the car is 270.5. Cheers Mariner - I was taught mental DR and nav in 1979 by a guy who flew in WWII..:ok:

UniFoxOs
26th Mar 2008, 15:33
Plugging the figures into the formulae off the web page quoted by SRT gives distance as 164.65 KM, bearing of car from starting point to be 87 deg (to nearest whole degree) so bearing of starting point from car must be 267.

UFO

(Also distance is 102.31 miles, AA)

Mariner9
26th Mar 2008, 15:36
Assuming your original maths was correct aa, and 85.5 is the correct bearing of the car from the starting point, I think you'll find the bearing from the car to the starting point should be 265.5 ;)

er340790
26th Mar 2008, 15:52
...... line up 100 navigators end-to-end and you'll never reach your destination!:E

mental DR???? Think I'll stick with deranged pilotage.

OverTq
26th Mar 2008, 16:34
What do you get if you cross a navigator with an Air Traffic Controller?

A bad letdown at the wrong airfield!

Rightbase
26th Mar 2008, 16:37
Airborn_artist has the best diagram.

UniFoxOs gets the same answer as me (after correcting my two detected errors).

There are lots of key presses involved, so the possibility of error is high. To verify for yourself, I get the following lengths:

Triangle 1 - 128, 102.225, 77.032
Triangle 2 - 93, 62.229, 69.112
Triangle 3 - 164.454, 7.92, and by Pythagoras, 164.6446

I calculate the top angle of triangle 3 to be 87.24 degrees, which makes the true bearing of the start point 267.24 degrees.

But check the context with your customer. The school exercise might be a test of how well she can use a protractor to draw a scale diagram.

BAMRA wake up
26th Mar 2008, 20:10
By Autocad - Airborne Artist's right angled triangles with lengths and angles added.

http://i300.photobucket.com/albums/nn38/bamra1/Navpuzzle.jpg

R J Kinloch
26th Mar 2008, 21:33
You guys (And PPRUNE) Rock!!!!!!!!

Many thanks from my daughter:)

Pontius Navigator
26th Mar 2008, 21:45
Is the bearing rhumb line or great circle?

helimutt
26th Mar 2008, 22:06
funny I thought the same as Pontius.

Solid Rust Twotter
26th Mar 2008, 22:15
Hence the supposition the question was about simple geometry rather than spherical as it was assumed Mr Kinloch was doing his daughters homework...:E

Blues&twos
26th Mar 2008, 22:29
I got 166km with a bearing of 260 deg from the final car position to the start point.....

The rusty brain-wheels of trigonometry have slowly started turning again.

Not sure whether this is right or not.....but my bit of scrap paper has got drawings on it now which are the same shape as those posted earlier, so that's got to be a good thing, right?

Miraculix
27th Mar 2008, 08:52
The earth is flat, I tell you! All these confusing math problems have been made to hide the fact, that the earth is flat! The govements of the western contries are spreading chemicals to control peoples minds.

Well at least Kinloch's daughters mathpaper should be flat ;)

GOLF_BRAVO_ZULU
27th Mar 2008, 10:47
At what Latitude is this journey taking place? We should be told.