Question

A surveyor starting from a point A moves N. 25°27' E. a distance of 523' 10.5" to point B. Next, she moves N. 49°29' E. a distance of 319 4.75" to point C. Next, she walks S. 6°2' W. a distance of 1292' 10.75" to point D. Finally, she returns to the starting point. What distance must she walk to return to the starting point? (Answer accurate to the nearest quarter inch.) feet & inches What heading does she walk from the fourth point to return to the starting point? (Answer accurate to the nearest minute.) N W. What is the acreage of this plot of land? area = acre Your answer should be accurate to 3 decimal places. Notes: * the prime symbol in an angle represents minutes: 60' = 1° * the prime symbol in a length represents feet; double prime = inches; * 1 acre = 4840 yd * 1 acre = 43,560 ft? * an angle like N 20 E means 20 degrees east of north.

Answer 1

to solve such question easily first compute total dorth direction movement and then total east direction movement u also called lectitiede & departure respectively. 1. Totoof nopen movement = 523.075 Cos(25°27') + 319.395860849°20') + 1292.8958 Cos (196°2') = -605.19423 feet Total east movement = 523.075 Sin(25*27') + 31913958 sin (49°29') +1292.8958 sin (196°2') = 332.03090 feet

1. To understand above two eq see the C E 1929 How 1602 319.39.00 Ra 1523.275/ • - ve sign in total north movement shows that the peint's is in south of point 'A' (-ve north 11292'10.75" – 1292.29507 value means value (Here, I have in south direction.) converted incha to •Distance must walk feet in points) c05.19428 Tona to return A will be - DA - / 605.194237332038902 DA = 690.29699 feet = 690!3.56" ~ 690' 3.5" Ans. Inne W 332.03898 tan o = 332.03892 605. 19423 To= 20° 45' so To reach point A from D see need to move at heading N 28° 45'w

area break it into a tre angles A BAO & ABCD To compute the ABAD (BADE 1000-25°271 BCD . c 2450 24327 1. - 20°451 319.3950 B CBCD=49897 Leer 6 2017 = 43°27' A 523.875 <BAD= 125% 125401 690.297 1292.8950 Area of trangle = 1/2 (AB) (AD) sin(BAD) { Area of the angle o = {*(BC) Cen) sin (<BCO) = **523.0750690.297 Sin (125°48') = {x 319.3950x1292.89958 sin(4327') = 146652.2371 sq; feet : 14199517051 sq.feet so total area =(146652.237 * 141995.7051 ) sq feet = 208647.9422 sq.feet. .: Area of plot = 200647-9442 = 6.62644 Acre - 43560 Aug

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