Question

In an orienteering competition , jada walks N70W for 200 meters. she then walks due eat for 90 meters. how far and at what bearing is jada from her starting point?

Answer 1

Answer:

219.3m, S24.2W

Step-by-step explanation:

The attached diagram shows the representation of the movement.

using Cosine rule to determine the distance from the starting point we have

$C^{2}=a^{2}+b^{2}-2abcosC\\C^{2}=200^{2}+90^{2}-(2*200*90)cos90\\C^{2}=40000+8100-(36000)*0\\C^{2}=48100\\C=\sqrt{48100}\\C=219.3m$

Hence the distance from her starting point is 219.3m

To determine her bearing from the starting point, we first solve for the angle y in the diagram using sine rule

$\frac{c}{sin90}=\frac{200}{siny}\\ \frac{219.3}{sin90}=\frac{200}{siny}\\ siny =0.911992\\y=sin^{-1}(0.911992)\\y=65.8^{0}$

$90-65.8=24.2^{0}$

Hence her bearing from the starting point is S24.2W