Trigonometry question

[jbetz]

Two cars A and B are parked back to back in the desert, one facing East, the other West.
Car A sets off and drives 5 Km in a straight line West, makes a 90° turn left and drives for a further 4 Km before making another 90° right turn and stops after driving a further 3 Km.
Meanwhile, car B drives 7Km East, makes a 90° right turn and drives 2 Km before making a 90° left turn and driving a further 1 Km.
As the crow flies, how far apart are cars A and B?

[Azalian]

I make it 17.19 klicks.

[jbetz]

I came up with 17.11, (and others) but that was closest to your answer, If you could find the time to explain how you worked that out I'd really appreciate it.

Thanks

[jbetz]

I've had another look at this and think that if you add the East West directions and both cars drive south you can draw a diagram that lets you draw a line between car A's 1st turn and car B's 2nd turn giving a hypotenuse that forms an isosceles (both being equal) to the distance between them.
So I think it's 16.12Km?

[Azalian]

Yeah, I got one of the turns wrong.

Final triangle is short sides 16 and 2, hypotenuse will be 16.12 as you say.

[Slapshot]

16.12.......

[jbetz]

Nicely done Slapshot, always good to see a little humour.

[samak]

Interesting how if you walked in the right direction along the hypotenuse you would only need to walk 120m more than the east - west distance of 16km to get there. But if you went due east or west for 16km you would then have 2 km more to go north or south.
I think this explains why it takes me so much longer to get back from the pub than to go there...

[R1Geezer]

It's 16.12 km
it's the hypotenuse of a right angled triangle 16 base 2 High
They are 16k apart on the West/East line and 2 k apart on the North South line.

[Old_Geezer]

Agreed you have a 16, 2, 16.1245... right angled triangle, but have you taken into account the curvature of the globe ?