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To find the double area of the triangle ICD.
To find the double area of the triangle IDE.
To find the double area of the triangle IEF.
To find the double area of the triangle IFG.
To find the double area of the triangle IAG.
The bearings and distances of the sides, if required, might readily be obtained. For, having found the distances IA, IB, we have in the triangle IAB, two sides, and an included angle; whence the angle IAB and side AB may be found. The angle IAB applied to the bearing of IA, will give the bearing of AB. In the same manner the bearings and distances of the other sides may be found.
Being required to calculate the area of a field, the owner of which refuses permission to go on it, I choose two
all the angles of the field are visible. The bearing and distance of the stations, and the bearings of the angles, from each station, are as follow. What is the area of the field?
The station G bears from the station F. N 439 W. 20 ch.
FD N. 16 E. GD N. 601 E.
Ans. 33 A. 1 R. 7 P.
LAYING OUT AND DIVIDING LAND.
To lay out a given quantity of land in a square form.
Reduce the given quantity to chains or perches and extract the square root, which will be the length of a side, of the same denomination to which the given quantity is reduced.
1. Required the side of a square that shall contain 9 A. 3 R, 28 P.
2. Required the side of a square track of land that shall contain 3.5 acres. Ans. 57 Chains.
To lay out a given quantity of land in a rectangular form, having one side given.
Divide the given content by the length of the given side, the quotient will be the length of the required side.
1. It is required to lay out 120 acres in a rectangular form, the length of one side being given, equal 100 perches.
192 perches, the length of the other side,
2. The length of a rectangular piece of land is 8 chains; what must be its breadth, that the content may be 5 acres. Ans. 6,25 chains.