- butterflydreamer

:) help with a bearing question please:
Uluru is a large rock on flat ground in Central Australia. Three tourists A, B and C are observing Uluru from the ground. A is due north of Uluru, C is due east of Uluru, and B is on the line-of-sight from A to C and between them.
The angles of elevation to the summit of Uluru from A, B and C are 26 degrees, 28 degrees and 30 degrees, respectively. Determine the bearing of B from Uluru.

- chestercat

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- butterflydreamer

I tried drawing a diagram but i'm not sure if it's correct LOL.
|dw:1436005924386:dw|

- anonymous

just want to say one thing .nice name of rock (uluru):P

- butterflydreamer

LOL it's a legitimate landmark HAHA

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- anonymous

lol.okay

- anonymous

wtf

- Empty

Hahaha beautiful picture and not only that, I can confirm for you that it is correct, good job.

- Empty

So now how do we go about actually solving this? I suggest labelling variables for distances and seeing if you can write out equations using these, and see if it is possible to solve for what you want from them. I can help from there if you're still stuck.

- butterflydreamer

hmm okay so let's say:
OA = x
OB = y
OC = z
Then do i try to find values of x, y and z in terms of tan ?

- butterflydreamer

|dw:1436006892249:dw|
So like let OP = h ...
x = h/ tan 26 etc...?
LOL i'm lost

- ali2x2

I wish i was that smart O.o

- Empty

Hmmm so suppose that you had this situation from birds eye view: |dw:1436007634363:dw| then A and C would have the same elevation instead of 26 and 30 separately right?

- butterflydreamer

yesss

- butterflydreamer

Not really sure where we're going from there .....

- Empty

Hmm, well I'm sorry to say I like being vague but at the same time I think you're the kinda person who really enjoys a challenge so I don't wanna give it away for your sake either.
Here's a hint
\[u= y \tan (28 )\] where u is the height of Uluru rock.
Try expressing other things in terms of trig functions, remember all we want to know at the end of the day is the value of y.

- butterflydreamer

oohhhhhhh right! Those were very helpful tips xD Thanks :)

- butterflydreamer

wwait.. At the end of the day, we're trying to find the bearing of B from Uluru

- Empty

Errr whoops my bad. #_#

- butterflydreamer

xD it's okay..

- Empty

Well what I mean is that we are looking for the slope of this line here

- Empty

|dw:1436009910357:dw|

- Empty

|dw:1436009997967:dw| The point we want lies on this line which we want the bearing of

- Empty

I feel like I've sorta said this in too confusing of a way by making a mistake in what I said ugh sorrry

- butterflydreamer

so far, all i've worked out is that z = sqrt 3 xD ...

- Empty

Oh how'd you manage that?

- butterflydreamer

well if we focus on |dw:1436010228446:dw|

- Empty

I don't think we're actually able to calculate any distances here, only relative distances since we weren't given any distances to begin with. I see, so if you are saying that uluru is 1, then yeah we can calculate distances relative to this unit height. :D

- butterflydreamer

ohhh jokes!
You can solve this using the area of triangles AOB, BOC and AOC :')

- butterflydreamer

thank you @Empty :)! ((also thanks for being patient LOOOL. My brain is lagging today))

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