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## Finding the bearing

I have encountered this question and am not sure how to answer it?
A hiker walks 3.2 km on a bearing of 120° degrees and then takes a bearing of 55° degrees and walks 6 km. The bearing he must take to return directly to the start is?

Break it down to how much he's moved East-West and North-South

3.2km at 120 degrees means he has moved:

• 3.2 sin(120) = 1.6 * sqrt(3) or ~2.77 (rounded) km to the North
• 3.2 cos(120) = 1.6 km to the West (you will get a negative number so it means you're heading West instead of East)

6km at 55 degrees means he has moved:

• 6 sin(55) = ~4.91 (rounded) km to the North
• 6 cos(55) = ~3.44 (rounded) km to the East

Total net movement:

• 2.77 + 4.91 = 7.68 km to the North
• 3.44 - 1.6 = 1.84 km to the East (West movement and East movement cancelling out)

Now you have a right-angled triangle with a base of 1.84, and a height of 7.68.

The angle bearing is tan (7.68 / 1.84) = tan (4.17) = ~76.5 degrees (may be off for the last decimal point depending on how many digits you rounded at)

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