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lorasvet [3.4K]
3 years ago
11

In an orienteering competition , jada walks N70W for 200 meters. she then walks due eat for 90 meters. how far and at what beari

ng is jada from her starting point?

Mathematics
1 answer:
shusha [124]3 years ago
7 0

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

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