Bearings

Subject: Compulsory Maths

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Overview

A compass always points north. Bearings are measured from the north line, always in a clockwise direction.A scale drawing is an enlarged or reduced drawing of an object that is similar to an actual object. Maps and floor plans are smaller than the actual size.

Bearings

Bearing

The bearing is an angle measured clockwise from the north direction. If you are travelling north, your bearing is 000°. If you are travelling in any other direction, your bearing is measured clockwise starting from the north. In the figure, the different direction shown by a compass are sketched.

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Example 1

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Note that the first two bearing above is in directly opposite direction to each other.They have a different bearing, but they are exactly 180° apart as they are in opposite direction.

A line in the opposite direction to the third bearing above would have bearing of 150 because 330°-180°=150°

These bearing in the opposite direction are called back bearing or reciprocal bearing.

Example 2

Find the bearing for:

Scholarships after +2 Abroad Studies Opportunities
  1. East(E)
  2. South (S)
  3. South-East (SE)

Solution:

  1. The bearing of E is 090°
  2. The bearing of S is 180°
  3. The bearing of SE is 135°

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Things to remember
  • A bearing is an angle, measured clockwise from the north direction.
  • Bearings are a measure of direction, with north taken as a reference. If you are traveling north, your bearings is 100°.
  • Using bearings, scale drawing can be constructed to solve problems.
  • It includes every relationship which established among the people.
  • There can be more than one community in a society. Community smaller than society.
  • It is a network of social relationships which cannot see or touched.
  • common interests and common objectives are not necessary for society.
Questions and Answers

Solution:

We can extend the line from A to B, then rotate through 180° to head in the opposite direction.

We can see from the diagram above that the bearing from B to A is 300° because 120° + 180°=300°

Solution:

Here, bearing from point A to B =\(\angle\)NPB =55o

Solution:

Here, bearing from point P to B=\(\angle\)NPB =105o

Solution:

Here, bearing from point P to B

=360o- \(\angle\)NPB

=360o- 70o

=290o

Solution:

Here, bearing from point P to B

=360o-\(\angle\)NPB

=360o-90o

=270o

Solution,

Here, Bearing from X to Y = \(\angle\)NXY = 60o

\(\angle\)NXY+\(\angle\)XYN' = 1800 [NX||N'Y]

or, 60o+ \(\angle\)XYN' = 180o

or, \(\angle\)XYN' = 180o- 60o

\(\therefore\) \(\angle\)XYN' =120o

Therefore bearing from Y to X = 360o-120o=240o

Solution:

Here, Bearing from X to Y =\(\angle\)NXY=90o

\(\angle\)NXY+\(\angle\)XYN'=1800 [\(\therefore\)NX||N1Y]

or, 90o+ \(\angle\)XYN'=180o

or, \(\angle\)XYN'=180o- 90o

\(\therefore\) \(\angle\)XYN'=90o

Therefore, Bearing from Y to X=360o- \(\angle\)XYN' = 360o- 90o=270o

Solution:

  1. North(N) and North-West(NW)

    =90o+180o+45o

    =315o

  2. North(N) and South-East

    =90o+45o

    =135o

  3. North(N) and West-North-West(WNW)

    =270o+22.5o

    =292.5o

  4. East-North-East(ENE)

    =45o+22.5o

    =67.5o

Solution:

Bearing of a stream = 120°

Again, when reaching to the plain bearing = 200°

∴ Change of flowing stream= 200° - 120° = 80°

Solution:

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Let Temple be A and School be B

According to question,

Bearing of point B =\(\angle\)NAB =62o

Here, \(\angle\)NAB + \(\angle\)ABN'=180 [ (\(\therefore\) AN||BN']

or, 62o+\(\angle\)ABN'=180o

or, \(\angle\)ABN' = 180o- 62o

or, \(\angle\)ABN' =118o

Now, Bearing from B to A =360o- \(\angle\)ABN'

= 360o-118o

= 242o

Solution:

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Let, Ship = BFrom point A bearing of the ship, is shown in the figure.

From point A bearing of the ship, is shown in the figure.

Solution:

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Let, School be M and Temple be N

Bearing from School to Temple =280ois shown in the figure.

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