Math Is Fun Forum

jesjesjesjes

Member

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.

http://imageshack.com/a/img856/5523/474g.jpg

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

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

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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

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

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

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igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

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

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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

John E. Franklin

Member

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.

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igloo myrtilles fourmis

Bob

Administrator

Registered: 2010-06-20

Posts: 10,624

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

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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

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

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.

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igloo myrtilles fourmis