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#1 2014-02-23 05:46:30
- jesjesjesjes
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- Registered: 2014-02-08
- Posts: 4
Bearings in math?
A rally car drives at 140 km/h for 45 minutes on a bearing of 32 degrees and then 180 km/h for 40 minutes on a bearing of 317 degrees. Find the distance and bearing of the car from its starting point. I was able to find the distance correctly, but I keep getting 137 degrees as the bearing. The correct answer is 352 degrees. This is what I've done so far.
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#2 2014-02-23 06:29:28
- Bob
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- Registered: 2010-06-20
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Re: Bearings in math?
hi jesjesjesjes
Welcome to the forum.
I agree with your distances: 105 and 120.
Now for the working:
easterly should be 105sin(32) - 120sin(43) = -26.1983 (so the car is further west than your sketch shows)
northerly should be 105cos(32) + 120cos(43) = 176.8075
I make that distance 178.7379. Is that what you got?
Then I did inv tan of 176.8075/26.1983 added 90 to get 148.7195 for the bearing.
Hmmm. Not the same as either answer.
I'll just check my working .......
I put a + sign rather than a * when converting from radians. See below for correct version.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#3 2014-02-23 06:31:47
- John E. Franklin
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- Registered: 2005-08-29
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Re: Bearings in math?
I get 351.57 degrees.
26.19827 West and
176.807 North.
176.807 = 89.045 + 87.7624 Vertical
26.19827 = 55.6415 - 81.8398 Horiztonal
igloo myrtilles fourmis
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#4 2014-02-23 06:35:50
- Bob
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Re: Bearings in math?
hi John,
I see I've not interpreted the question correctly. I worked out the bearing to get back home so I should get the right answer by + 180.
But I don't. ??
still checking.
I get that distance using the cosine rule too.
Just recalculated the angle and I get the same as John now, 351.5716
jes: Your diagram makes me think you tried to use cosine rule and sine rule for this. John and my method is easier and safer.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#5 2014-02-23 06:45:07
- John E. Franklin
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- Registered: 2005-08-29
- Posts: 3,588
Re: Bearings in math?
I broke the question into a right triangle for the 105 hypotenuse and the 120 hypontenuse.
I just use hypotenuse times cosine angle for adjacent run,
and hypotenuse times sine angle for opposite perpendicular run.
igloo myrtilles fourmis
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#6 2014-02-23 06:46:43
- Bob
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Re: Bearings in math?
Yes, me too. I've put a comment for jes in my previous post about that. My error was a plus sign that should have been times.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
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#7 2014-02-23 06:49:16
- John E. Franklin
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Re: Bearings in math?
Inverse Tangent is also useful when you know the final north and west components.
inverse tangent of 6.7488, where 6.7488 is north component / west component
inv tan(6.7488) = 81.5715 degrees
and then since it was NNW, I added 270 degrees = due west.
igloo myrtilles fourmis
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