Question

A student walks 50 m on a bearing 025° and then 200 m due east. How far is she from her starting point?​

Answer 1

Bearing is degrees from north, so we have a triangle ABC where AB=50m is 90-25=65 degrees to the horizontal, A being the starting point. BC=200m is horizontal. AC is the distance we need to find.

Angle ABC is 90+25=115 degrees so we can use the cosine rule to find AC.

AC^2=AB^2+BC^2-2AB.BCcos115=2500+40000+20000cos65=50952.365 approx.

AC=√50952.365=225.73m approx.