Help with bearings

[jm1234]

I am seeking help for the following problem:

A hiker walks 8000 m on a course of S 81 degrees E. They then change direction and hike 5000 m on a course of N 32 degrees E. How far are they from their starting point and on what course must they travel to return to the starting point.

 

[Dr.Peterson]

Where do you need help? And what methods are you expected to use (vectors, coordinates, trigonometry, ...)?

I'd start by sketching the situation, marking the given values and what I need to find. Have you done that? Please show it to us.

If your difficulty is in interpreting the bearings, S 81° E means 81° toward the east from south, which will be a direction just a little below east; and N 32° E means you draw a line to the north, and make an angle 32° to the east of that, which will be sort of northeast (up and to the right).

 

[Aliabla]

The problem forms a triangle you need to use either the law of cosine or sine to find the answer.

 

[Dr.Peterson]

Yes. So what is the triangle, and which rule have you tried using? You aren't showing much beyond that you are using trigonometry.

We need to see where you need help. That's why I asked you to show your drawing, or something to let me know if you can get at least that far. Are you implying that you don't know how to draw the triangle?

I'll be generous and make a drawing for you (yours can be a mere pencil sketch):



I've shown the given bearings; you have to find angle theta and distance x. Can you see how to find angle ABC, and which law to use to find x?

 

[Probability]

Using Dr Peterson's diagram and the Cosine rule, you should be able to find x.

AC^2 = BC^2 + AB^2 - 2 x BC x AB x cos ABC

AC^2 = 5000^2 + 8000^2 - 2 x 5000 x 8000 x cos 122

AC^2 = 131393541

AC sq = 11462 m

One then must always ask is the answer reasonable!

Well there are three sides to the diagram 5000 and 8000 and the longest side calculated now is 11462, hence the answer seems reasonable.

 

[Dr.Peterson]

There's a mistake there. Where did 122 come from?

Of course, the goal here was to get @jm1234 to do this himself, in order to learn to think. So please leave that uncorrected.

Then, he still has to find the angle.

 

[Aliabla]

There's a mistake there. Where did 122 come from?

Of course, the goal here was to get @jm1234 to do this himself, in order to learn to think. So please leave that uncorrected.

Then, he still has to find the angle.

Exactly my thoughts too Dr Peterson.

 

[Probability]

There's a mistake there. Where did 122 come from?

Of course, the goal here was to get @jm1234 to do this himself, in order to learn to think. So please leave that uncorrected.

Then, he still has to find the angle.

You'r correct its much less but as you say I'll leave it. I suppose its ok to advise the OP to look at the sin rule for his angle measurement.

 

[Dr.Peterson]

If the OP still hasn't responded in a couple days, it will be reasonable to show more. It's unfortunate that a lot of people abandon their good questions without ever interacting with us.