Bearing Help- Maths (1 Viewer)

[ellie95]

Hi Everyone, Ellie’s Sister again and I’m in need of helpwith these bearing questions for maths. Could you please show me via a diagram (picture)with solutions please.
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1. A large rock is sighted by Emilie at N56^oWfrom her original position. After travelling due west for 153 km, Emilie nowsights the rock as being due north of her.
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i) How far from the rock is Emilie now?
ii) How far from the rock was Emilie’s originalposition?
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2. Julia travels 58 km due south and then turns andtravels due east. After a while she stops and takes a bearing back to herstarting point and finds that its bearing is 310^o from her presentposition.
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i) Find the distance that Julia travelled east
ii) Find the distance (in a straight line) that sheis from her starting point
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3. You are planning a trip on your boat. If youtravel 20 km from A to B on a bearing of 42^o T:
a) How Far East of A is B?
b) How far north of A is B?
c) What is the bearing of A from B?

 

[HSC2014]

These are pretty simple bearings questions. If you can't do those I think you need to re-learn bearings and trigonometry, not much that I can help with (providing answers isn't useful in this scenario).
Anyway for the first question:
1. Plot Emilie's original point.
2. Construct a line N 56 W to a point which is the rock (This will result in an acute angle of 34 in the triangle)
3. Construct a line west (153km) from the original point, so that the line extends to under the rock
4. You now have a right angled triangle and you can work from there Use trigonometry to find the answer.

 

[ellie95]

These are pretty simple bearings questions. If you can't do those I think you need to re-learn bearings and trigonometry, not much that I can help with (providing answers isn't useful in this scenario).
Anyway for the first question:
1. Plot Emilie's original point.
2. Construct a line N 56 W to a point which is the rock (This will result in an acute angle of 34 in the triangle)
3. Construct a line west (153km) from the original point, so that the line extends to under the rock
4. You now have a right angled triangle and you can work from there Use trigonometry to find the answer.

By the way I'm only in year 9 and just learning it. I know how to do trig I just need to improve on bearings, which will happen over time

 

[enoilgam]

By the way I'm only in year 9 and just learning it. I know how to do trig I just need to improve on bearings, which will happen over time

Bearings is probably the most difficult part of year 9 trig, so its not uncommon for people to struggle with these kinds of questions. The most difficult part of these questions is probably doing the drawings.

 

[HSC2014]

Oh I thought you were in year 10 :L For bearings, it is important to have a good sense of placement when interpreting the question. It's best just to draw it out as you go along the question. I'll do a step-by-step process on how to do question two. This should be applicable to any question once you understand it.

Julia travels 58 km due south and then turns and travels due east. After a while she stops and takes a bearing back to her starting point and finds that its bearing is 310^o from her present position.

First, we always have a starting point. This is where sense of placement comes in useful. You have to know the general direction the question is going in, otherwise if you start on the left of your page, the question might unfold to the left, leaving no room for you!

So firstly, Julia travels 58km south. Construct this line and label it 58km. I marked the starting position with a red dot.

Now, reading along the question we find out that she travels east for an unknown distance. Construct this line. (Travelling south and then east forms a right angle. I forgot to mark this!)

The final part is a bit tricky since it involves angles and what not. We know she walks back to her starting distance, thus completing the triangle. Reading the question carefully, it states that the original position is 310^o FROM the point where she stopped before heading back to original position. This can be interpreted like.. pretending you are standing at the stopping point, facing north. The path to original position would be 310 degrees from you. Whenever you see i.e. Home is x degrees from House. This means that, standing at the house facing north, home would be in a direction that is x degrees from you. So now we draw in a compass (north,east,south,west)? at the stopping point and show that the line back to home is on a bearing of 310^o You will get confused with this part countless of times, but practise makes perfect.

Now since we know that the west direction is 270^o, we can find the angle inside the triangle by 310^o-270^o = 40^o.

Then trigonometry magic to find your answers

Edit: Yes, bearing is definitely one of the harder topics of year 9 maths alone. I personally struggled with it until year 10 (I sometimes still get confused!). The trick is to read the question carefully and being able to map out the points that they point out and using deductive skills to find necessary angles and what not (alternate angles, corresponding, etc).