Central Luzon State University - MATH GEOMETRYDetermination of Area of a Rectilinear Field by Tape_Laboratory Exercise.

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EXERCISE NO. 4: Determination of Area of a Rectilinear Field by Tape Introduction Measuring a field is a complex and time-consuming task. The sides of a field are usually measured with a measurin... g tape or chain, and the angles of a field with a compass. In surveying a field for the purpose of finding its area, the instruments and methods used will be determined largely by the degree of accuracy required. If it is permissible to have an error in the area of, say, 0.5 per cent then the compass and chain may be used. If accuracy much greater than this is required, it will be necessary to use the transit and the steel tape. At the present time, however, in nearly all work except surveys of farms and wood-lands, the transit is used even under conditions where the compass would give the required accuracy. In surveying a field all the angles and lengths of the sides are determined consecutively, the survey ending at the point from which it was started. Then by trigonometry the position of the final point or of any other point with relation to the starting point can be readily calculated. If the survey were absolutely accurate the last point as calculated would coincide with the first, but this condition is never attained in practice. The calculated distance between the two, divided by the perimeter of the field, is usually called the error of closure - it is often expressed in the form of a fraction in which the numerator is unity. Objectives  To learn how to read the horizontal angle of a total station.  Improve skills in the analysis of the area of right triangle. Procedure  Assign a centre point, mark with a range pole.  From the centre point, use the tape measure to make a line of more than 20 metres then mark the end with a range pole. Repeat 5 times, each line a different direction than the others. These lines will be the sides.  On each side, measure 20 metres from the centre.  From the 20 metre mark on the first side, measure the distance across to the 20 metre mark of the second side. Repeat until it reaches the first 20 metre mark. Each side will form a triangle.  Measure the angle of each formed triangle using the formula: sin θ 2 ¿ d 2 L  Then, measure the area using the formula: A= 1 2 ( a¡)(b ¡) sinθ¡ [Show More]

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