Expert: Paul Klarreich - 5/26/2008

Question
The question is to measure a inaccessible point. If, lets say one point is on the other side of a river and you need to survey the area. So you form a triangle thats not have a right angle. Two of the three sides and the angle between these two sides is known to you. How to work out the other two angle's and the third side.

Answer
Questioner:   DRICUS
Category:  Advanced Math
Private:  No
 
Subject:  triangleation
Question:  The question is to measure a inaccessible point. If, lets say one point is on the other side of a river and you need to survey the area. So you form a triangle thats not have a right angle. Two of the three sides and the angle between these two sides is known to you. How to work out the other two angle's and the third side.
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Hi, Dricus,

You use either (or both of) the

Law of Sines -- if an angle and the side opposite that angle are both known.
Law of cosines -- otherwise.

If the angles are called A,B,C, then the sides opposite them are a,b,c.  [a is opposite A, etc.]

If, as you say:  "Two of the three sides and the angle between these two sides is known to you"

then you have, say,  a,b,C;  C is between a and b.


and you do NOT have an angle-and-opposite-side known, so you will start with the Law of cosines.  That will give you c.  AFTER that, you will have c and C, so you can now use the Law of Sines to finish up and find A and B.