. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. DIVISION OF LANDS. 125 triangle into two parts in the ratio 2 to 3, by a line running due eastand west. Let ABC be the given triangle, and BCthe required division line. It is required tofind the numerical value of A C or AB, tomake the area ABC § of the area ABC. Let b represent the side of the triangleopposite B, and c the side opposite C. Let A C=x. As A C and, OB have defi-nite directions, the angle ACB is given,also ABC is given. ACB^%0, ABC=65°, BAC=67°. In the
. A treatise on surveying and navigation: uniting the theoretical, the practical, and the educational features of these subjects. DIVISION OF LANDS. 125 triangle into two parts in the ratio 2 to 3, by a line running due eastand west. Let ABC be the given triangle, and BCthe required division line. It is required tofind the numerical value of A C or AB, tomake the area ABC § of the area ABC. Let b represent the side of the triangleopposite B, and c the side opposite C. Let A C=x. As A C and, OB have defi-nite directions, the angle ACB is given,also ABC is given. ACB^%0, ABC=65°, BAC=67°. In the triangle ABC we have. sin. 65° : x : : sin. 48° : AB Whence AB= -r sin. 48° (1) sin. 65° Now, by Prob. Ill, Mens., area ABC=\bc sin. A. /sin 48°\Also, area ABC=\[ gin 65Q Jx* sin. A By the conditions of our problem, we have the following pro-portion. be sin. A : I /sin. 48°\\sin. 65°) x2 sin. A : : 5 Or, sin. 48°sin. 65° (2) We may here stop, and make the problem general. If B C is given in direction, the angles B and C will be given. We now require the division of the triangle ABC into two parts,in the ratio of m to n by a line opposite to the angle A, running ina given direction. Represent the sides of the given triangle adjacent the angle Aby b and c, b extending from A to B, and c extending from A to C. Put x= the distance from A to the division line, on the side CA. Then, by the preceding proportion we have, 126 SURVEYING. sin. C be : -i &X2 : : m-J-w : m sin. i> l __ /m-\-n\\/bc sin. if \ Whence, ^—.^^—.J Observe that x is opposite the angle B, the sine of which standsin the numer
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Keywords: ., boo, bookcentury1800, booksubjectnavigation, booksubjectsurveying
