Simultaneous equations approach to projectile motion problem

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Homework Statement



Diagram of a ship sailing east toward a light, with two right triangles sharing the vertical height y; angles 27°50' and 41°35' at the base, base segments labelled 2250 and x, and equations tan(27°50') = y/(2250 + x) and tan(41°35') = y/x.



Homework Equations





The Attempt at a Solution



I just derive two equations and solve simultaneously. It delivers the correct answer of 2933.5m. But it is a bit of a long method, can anyone see an easier way?
 
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  • Diagram of a right triangle with a horizontal base split into 2250 and X, a vertical side labelled Y, and angles 27°50′ and 41°35′ at the base; two tan equations are shown alongside.
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Without seeing your work we can not tell if it can be done simpler.ehild
 
Sorry, what I mean is; is there any non-simultaneous way to solve this?
 
There is nothing wrong with your method. You might consider the law of sines for an alternative.
 
voko said:
There is nothing wrong with your method. You might consider the law of sines for an alternative.

Ok, cool. But that would still involve a simultaneous equation.
 
memoguy said:
Ok, cool. But that would still involve a simultaneous equation.

Why is it a problem? It is simple to solve. Show what you did.

Introduce the variable y/x. Or divide the equations with each other.

ehild
 
memoguy said:
Ok, cool. But that would still involve a simultaneous equation.

I do not think so.
 
ehild said:
Why is it a problem? It is simple to solve. Show what you did.

Introduce the variable y/x

ehild
No problem at all. Just that someone I was talking to kept saying that I was over thinking it by solving simultaneous but I just can't see how to get around that.

voko said:
I do not think so.

Ohh! How?
 
memoguy said:
Ohh! How?

What does the law of sines say?
 
voko said:
What does the law of sines say?

sin(A)/a=sin(B)/b=...
 
In your problem you have three points: the point of the first sighing, the second sighting, and the light itself. Let's call them A, B, C.

Can you find the length of AC or BC?