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A triangular shaped area on the corner of North and East Road is to be acquired by the road authority as shown in the diagram.

The circular arc AC starts at the tangent point A in North Road 88.44m west of the intersection and cuts the East Road boundary at C 27.52m from the corner.

Using geometry and trigonometry find:-

1. Radius, Arc Length, Chord Bearing and Distance of the arc AC.

2. The area of land ABC cut off by the arc AC.

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  • The instrument station at point A is set up over the intersection of the centreline of the 30m wide road bearing 32°50'and the 20m wide road bearing 105°36'.
    CB and BE are extensions of the road boundaries intersecting at B.
    The centreline of the 20m road bearing 315° passes through point B.

    Compute the bearing and distance of the setout lines from station A to corner points B, C, D and E.


    • Something a little easier.
      A large culvert passing under Argus Road discharges into a stream passing through the rectangular property ABCD.
      The stream is to be contained within a parallel-sided easement 10m wide located as shown in the diagram.
      Compute distances AE, EB, bearing and distance AF and the area of the easement.


      • ABCD represents the curvilinear alignment of a road centreline.
        The 150m radius between BC is to be replaced by a 300m radius EF.

        Compute the arc length, chord bearing and distance of the 300m radius curve.
        How much shorter is alignment AEFD compared to original alignment ABCD?
        Find the maximum displacement X between the two alignments.


  • Land Surveyor

    Neat problems you are posting. I don't see any replies so if I get a chance today I will take a hard look at them and see if I can come up with some solutions. Love these brain teasers though. 

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