# Mathematics

Sketched this Bearing
A survey leaves a base camp and drives 42km on a bearing of 032 degree, she then drive 28km on a bearing, if 154 degree. How far is she from her base?

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1. You take a bearing. You travel on a heading.
DRAW THIS !!!
call starting point A
second point B at 32 deg from north toward east, 42 km
third Point C at 180 - 154 = 26 deg from south toward east
so Angle ABC at B is 32 + 26 = 58 deg
now we have angle of 58 deg between triangle lengths of 42 and 28
That is law of cosines to find the third side.
b^2 = a^2 + c^2 - 2 a c cos 58
b^2 = 28^2 + 42^2 - 2 * 28 * 42 * 0.53
solve for b

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