Elementary Surveying: An Introduction to Geomatics (15th Edition)
Elementary Surveying: An Introduction to Geomatics (15th Edition)
15th Edition
ISBN: 9780134645964
Author: GHILANI
Publisher: PEARSON
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Chapter 11, Problem 11.1P
To determine

The length of line AB, azimuth of AB , and bearing of AB.

Expert Solution & Answer
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Answer to Problem 11.1P

Thus, the length of AB=367.539m, the azimuth of AB=31°18'24.36", and bearing of line AB is N31°18'24.36"E .

Explanation of Solution

Given:

The coordinates of point A that is the station shore is (246.873,659.457) and the coordinates of point B that is the station rock is (437.854,973.482) .

Calculation:

Calculate the length of line AB .

  LAB=( X B X A )2+( Y B Y A )2     ....... (I).

Here, LAB is the distance between point A and point B, XA , XB are the x-coordinates of point A and B respectively and YA , YB are the y-coordinates of point A and B respectively.

Substitute 246.873m for XA , 437.854m for XB , 659.457m for YA and 973.482m for YB equation (I).

  LAB= ( 437.854246.873 )2+ ( 973.482659.457 )2= ( 190.981 )2+ ( 314.025 )2=36473.742+98611.701=367.539m

The length of line AB=367.539m .

The azimuth of line AB is determined by using the formula,

AzimuthAB=tan1(XBXAYBYA)+C     ....... (II)

Here, AzimuthAB is the azimuth of line AB, XA , XB are the x-coordinates of point A and B respectively, and YA , YB are the y-coordinates of point A and B respectively and C is a constant.

Substitute 246.873m for XA , 437.854m for XB , 659.457m for YA and 973.482m for YB equation (II).

Since (XBXA) and (YBYA) are greater than zero, the value of C=0° .

  AzimuthAB=tan1( 437.854246.873 973.482659.457)+0=tan1( 190.981 314.025)=tan1(0.608)=31°18'24.36"

Thus, the azimuth of AB=31°18'24.36" .

The bearing of AB is determined from the value of its azimuth.

Since AzimuthAB=31°18'24.36" , it lies between North and East, thus the bearing of line AB is equal to N31°18'24.36"E .

Conclusion:

Thus, the length of AB=367.539m, the azimuth of AB=31°18'24.36", and bearing of line AB is N31°18'24.36"E .

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