You are Here: Home >< Maths

# finding angles using one lenghs watch

1. sorry for the bad title but i don't know what this is called (why google wasn't any help )

four roads from a square with cornes P, Q, R and S. somewhere in the field is a barn, B. you know distances BP, BQ, BS

find the dimesnsions of the field and the location of the barn. show that there are two possible awnsers. comment on them

BP = 6.4
BQ = 9.2
BS = 17.5
this is a project for my first year at uni

any pointers, obviously i'm not looking for awsers it's just i have no idea how to do it, spent about on hour trying and getting no where.

i did try solving simultaneous equations but that didn't work. and i did try constructing a right angle S but couldn't make anything with it(although i think it's something like that)

would be great if someone could just post a link to something so i can help myself

cheers
2. Have you noticed it is a square so PS = PQ.

Cosine Rule, Pythagoras' Theorem and angles around a point = 360 degrees?
3. haven't thought about it throughly...
but i think it would be helpful if you draw circles from P,Q,S with the diameter of BP,BQ, and BS and if you find that there is indeed 2 points where all three points are intersecting then you are proving that there are indeed 2 possible answers.
4. as an engineer. i'd personally draw out the diagram to scale. and just measure off the answers...

that may not be exactly what you're looking for though
5. (of course you have to 'prove', not 'draw', they are intersecting )
6. the drawing was given to us, the aim to to find the length SP and the co-ordinates of B

still don't know what to do though, is this solved by simultaneous equations??
7. Who was it given to you by?

I briefly used dynamic geometry software to check your diagram as the length 17.5 looked suspiciously large to me and the barn lies outside the square. Sorry!
8. my lecturer, are you sure? maybe that was just the other theoretical solution??? the there is still a "real" solution that lies in the square perhaps?
9. There is no other solution. You can solve it if BS = 7.5 for example. Did you copy it down incorrectly? What degree is this?
10. it's printed, each group got a different data set

this is for a mathematics degree, and this is question 1 of three (although if you can do this one the others are probably not much harder)

11. Well consider this situation.

What is the maximum length of BS?

12. Hmm, so its not possible to be inside the field if its a straight line, what about if the barn was above or below ground? Could it then be inside the field as seen from a bird-eye point of view?

(I know this really doesn't help, but I read the thread and was interested.
13. (Original post by Rubgish)
Hmm, so its not possible to be inside the field if its a straight line, what about if the barn was above or below ground? Could it then be inside the field as seen from a bird-eye point of view?

(I know this really doesn't help, but I read the thread and was interested.
I considered that the barn might be up a hill but as the OP didn't know how to deal with this problem in 2D, I decided not to go there.

Spoiler:
Show
I should probably clarify that the words "I decided not to go there" do not mean I cancelled a visit to the barn.
14. Little out of my depth, but the fact you're going to get two answers says that it's going to have something to do with Trigonometric symmetry, i.e, . Which of course then suggests you're going to be using the circular functions. Looks like you can make a Right angle with PBS too, to find one side(and thus all 4 since it says it's a square)

That's all I got, and was pretty obvious, so sorry.
15. Spoiler:
Show
I should probably clarify that the words "I decided not to go there" do not mean I cancelled a visit to the barn.
So you're still planning on going?

I hear the Barn is lovely this time of year.
16. Applying Pythagoras three times, you can generate three equations with three unknowns, some of which are are squared. It certainly looks solvable and might even yield two solutions.

My three equations are:

Enjoy solving them. I hope there are real solutions and they have been set up right.

As an engineer, I too am inclined to plot that system (in Matlab, everyone hates rulers now) and just read off the answers. Being a maths student I expect you won't be able to sleep without finding the exact solutions.
17. (Original post by Henerz)
As an engineer, I too am inclined to plot that system (in Matlab, everyone hates rulers now) and just read off the answers.
As an engineer, are you too busy to read a thread properly before you post?

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 13, 2010
Today on TSR

### Top unis in Clearing

Tons of places at all these high-ranking unis

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams