Thread: find distance

i have a triangular plot of land through which a stream runs. the point B is due east of A and AB is 50m long. the bearing of C from A 026 degrees and the bearing of C from B is 328 degrees. calculate the distances AC and BC.

could this problem be solved in a alternative way? if so, describe an alternative method.
thanks
jim

Originally Posted by jim49990

i have a triangular plot of land through which a stream runs. the point B is due east of A and AB is 50m long. the bearing of C from A 026 degrees and the bearing of C from B is 328 degrees. calculate the distances AC and BC.

could this problem be solved in a alternative way? if so, describe an alternative method.
thanks
jim

If "bearing" means what I think it means, the interior angle of the triangle at A is 26 degrees and the interior angle of the triangle at B is 32 degrees. Is that right? Edit: No! The angles are 64 degrees and 58 degrees. In that case, I suggest you draw a line from C to a point D on the AB line chosen so that AB and CD are perpendicular.

CD/AD=tan(26 degrees)
CD/DB=tan(32 degrees)
AD+DB=50 m

Solve this for CD and use that CD=BC sin(32 degrees) and CD=AC sin(26 degrees).

Alternative method? This is the only one I can think of right now.

i think the answer is 50m

Hello, Jim!

I hope you understand "bearings" . . .

I have a triangular plot of land through which a stream runs.
Point B is due east of A and AB is 50m long.
The bearing of C from A is 26° and the bearing of C from B is 328°.
Calculate the distances AC and BC.

Code:

                        C
                        *
                     *   *
      :           *  58°  *   :
      :        *           *  :
      : 26° *               * :
      :  * 64°           58° *:
    A * - - - - - - - - - - - * B
                  50

Since and , then:

. . is isosceles: m.


Law of Cosines: .

Therefore: . m.

Apparently I got the angles of the triangle wrong. The method I suggested will get you the correct answer if you use the correct angles: 64 degrees and 58 degrees. So you can consider that the "alternative" method.

thanks for that. the fact that there is a stream is irrelavant..
jim