Bearings and trigonometry

trishyliz

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Please could anyone help me with this question
A party of geographers is out on a field trip. They start walking from a church on a bearing of 223o and walk in that direction for 3.5km to get to a lake. They then turn roughly east and walk on a bearing of 101o. After walking for 6.6km it starts to rain heavily and they decide to abandon the trip and head straight back to the church for shelter.
a) By creating a scale drawing, state how far away from the group the church is when it starts to rain heavily and what three figure bearing the group need to walk on in order to get back to it.
b) Discuss the effect of accuracy on the reliability of your answer to part a) and check your answer using trigonometry.
To complete this test you have to use some of the following formulas including:

This is what I have done already and I have also attempted to do a scale drawing but I dont think its right

Answer to Part B
The assumptions, which I have made is the north and east are positive directions.

The distance from North to the rain start point is:

3.5 cos 223 + 6.6 cos 101= - 3.819km

The distance from East to the rain start point is:

3.5 sin 223 degrees + 6.6 sin101degrees = 4.092 km

Distance back to the church shelter is:


d = √(4.092² + (-3.819)²

d = 5.6 km


So the bearing to follow is:
Travel 3.819 km North and 4.092 km East


tan θ = 3.819/ -4.092


θ = -43 degrees

By adjusting that to the origin and correcting for the quadrant


Bearing becomes θ = 313°

c) How long do you think it will take the group to walk back to the church? Explain and justify any assumptions you make.
We do not know what the walking speed is, but if we use Naismith’s rule, which helps in planning or a walking or hiking expedition, by calculating how long it will take to walk a route . This states to allow an 1 hour for every 5 kilometres and when walking in groups calculate for the speed of the slowest person. So I feel by calculating using this law it should take the group approximately about an hour and half to walk 5.6km.
 
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