Question 1110389: A bushwalker walks 8 km on a bearing of 116 degrees from L to M, then proceeds to walk a further 13km to N on a bearing of 026 degrees.
a) calculate his distance from L, correct to the nearest km.
b) find his bearing from L, correct to the nearest degree
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! If this is drawn out, it is a right triangle with LMN being a right angle.
One leg is 8, the other 13 and the hypotenuse is sqrt (233) or 15.26 km distance.
The bearing is tangent of L, which is two parts, known 26 degrees south of east plus another component north of east. That combined tangent is 13/8, opposite over adjacent, or 1.625. The arc tan (1.625) is 58.39 deg, making the missing angle 32.39 north of east or true bearing of 57.61 deg.
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