Solved Example-Distance of a Point from a Line, whose end Co-ordinates are given.

Hi,

Problem:
The X and Y coordinates(in meters) of station Shore are 246.87 and 659.46 respectively, and those for station Rock are 437.85 and 973.48, respectively. The azimuth, bearing, and length of the line connecting station Shore to station Rock are 31d,18 m, 24 s,  N31 d18 m 24s E, and 367.540 m, respectively.
What is the perpendicular distance of a point from the line if the X and Y coordinates of the point are 414.278 and 959.083, respectively?

Note:




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solved Example - Find the elevations at full and half stations along sag curve

Problem:
A -2.8% grade line meets a +3.6% grade line at station 125+00.  Elevation=1631.04 ft. Determine the elevation of all full and half stations if a 650-ft curve is to be used.

solution:

Solution of vertical curve length, that passes through a fixed point elevation - solved example.

Problem:
A -4% downgrade intersects a +3% upgrade at elevation 120.00 ft at station 95 + 00. it is desired to pass a vertical curve through a point of elevation 128.00 ft at station 96 + 00. determine the curve length required.

solution: