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Abrar Rana · May 20, 2007, 02:06 PM

Hi All

I am new to this site and want a solution to this problem related to bearing

A man swims 50 meters in the direction 045, then 60 meters in the diretion 145. How far is he from the starting point?

Thanks in advance to all participating who help me solve this problem

Regards

Abrar

galactus · May 20, 2007, 02:40 PM

Technically, these are azimuths, not bearings. By 045, I reckon you mean 45 degrees off true north or the y-axis? That's what I'm going with. If not, you can adjust accordingly.

Assume the starting point is at the origin and give it coordinates (0,0).

The swimmer then swims N45E for 50 meters. Find the coordinates of this point by using trig.

$x=50sin(45)=25\sqrt{2}, \;\ y=50cos(45)=25sqrt{2}$

Now, heading onward from here, the swimmer goes 145 degrees or S35E for 60 meters.

$x=25sqrt{2}+60sin(145)\approx{69.8}, \;\ y=25sqrt{2}+60cos(145)\approx{-13.79}$

Now, to find the distance from this point to the beginning, use Pythagoras:

$\sqrt{(69.8)^{2}+(-13.79)^{2}}=71.15 \;\ meters$

See how that works?

Stratmando · May 26, 2007, 06:09 AM

Interesting answer. Makes my head hurt.
I would draw it out on Paper and Measure the difference.
Would not be as accurate as above.

galactus · May 26, 2007, 10:13 AM

No, it wouldn't be as accurate, but depending on what you need it for your method may be good enough. In the case of surveying property, accuracy and precision is very important.
I have 'scaled' many a drawing and it was close enough.

brooklyngurl345 · May 27, 2007, 10:07 AM

Originally Posted by Abrar Rana

Hi All

I am new to this site and want a solution to this problem related to bearing

A man swims 50 meters in the direction 045, then 60 meters in the diretion 145. How far is he from the starting point?

Thanks in advance to all participating who help me solve this problem

Regards

Abrar

210 I don't know but it was fun trying lol ; )