How do I know what the author was thinking....

[Probability]

Suppose I present you with a question like this;

This is a vector question,

A man walks 6 km south - west and then 4 km due - west. How far, and in what direction, is he from his starting point?

This problem can be carried out by scale drawing and by calculation.

This is the problem I have with the question;

Draw the first bisector to represent the origin, no problem there, then the problem, draw the vector that shows the man walks 6 km south - West?

It isn't due south, so how do I know how to interpret the angle south - West the author had in mind, it could be any angle from 1 degree to 89 degrees and if I choose the wrong angle obviously the answer would be incorrect.

Is there a mathematical standard here that I am missing in these types of questions?

 

[stapel]

"A man walks 6 km south - west and then 4 km due - west. How far, and in what direction, is he from his starting point?"

This is the problem I have with the question: ...How do I know how to interpret the angle south - West the author had in mind...?

Unless you're told to interpret "south-west" as "south-west-ish, but really [some specified other angle]", you should assume that "south-west" means exactly what it says: exactly between "south" and "west".

 

[HallsofIvy]

Is this a language problem? If English is not your native language you may not know that "southwest" has a very precise meaning- it is exactly half way between "south" and "west"- 225 degrees on a compass.

(For your edification, exactly half way between "south" and "southwest", that is, at 202.5 degrees, is "south southwest" and half way between "west" and "southwest", 247.5 degrees, is "west southwest". I won't go into "west by south southwest", etc.)

 

[Probability]

Thank you for your replies, I didn't know how to interpret the mathematical understanding of South - West, I understand the direction, but didn't know mathematically how to correctly interpret it.

In my example here then I will take it that the author is saying after drawing the first bisector measure 45 degrees South - West, walk 6 km and then 4 km due - West. I have then drawn the resultant vector and this has measured 9.3 km. Mathematically I worked it out as 9.27 km.

Thanks:smile:

 

[stapel]

I didn't know how to interpret the mathematical understanding of South - West....

I will take it that the author is saying after drawing the first bisector measure....

Exactly. The common-usage English meaning of "southwest" often means "southwest-ish"; that is, in a direction somewhere between southerly and westerly. For instance, Interstate 30, going from Arkansas to Texas, would probably be said to be taking the traveller in a "southwesterly" direction, though the freeway is actually winding around in a more west-southwesterly direction. The lower leg of Interstate 79, in West Virginian, would also be termed (informally) as heading southwesterly, though it's clearly heading in more of a south-southwesterly direction. Interstate 85, paralleling the eastern seaboard, is closer to a heading of southwest. But it's hardly a straight line.

The above are all examples of "real world" meanings of "southwest". Clearly, they do not demonstrate any sort of mathematical precision. In your math homework, you're working with an "ideal" world, being one where the realities of topography, etc, do not come into play. In your word problems (and likely only in that context), "southwest" means "along the line y = x, for x < 0", or "forty-five degrees anti-clockwise from the negative x-axis".

 

[Probability]

In your math homework, you're working with an "ideal" world, being one where the realities of topography, etc, do not come into play. In your word problems (and likely only in that context), "southwest" means "along the line y = x, for x < 0", or "forty-five degrees anti-clockwise from the negative x-axis".

Thanks stapel, exactly right