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A, B, C and D are four towns.
B is 25 kilometres due East of A.
C is 25 kilometres due North of A.
D is 45 kilometres due South of
North
Not to scale
1
CX
AM
DX
Calculate the bearing of D from B.
(4 marks)

A B C And D Are Four Towns B Is 25 Kilometres Due East Of A C Is 25 Kilometres Due North Of A D Is 45 Kilometres Due South Of North Not To Scale 1 CX AM DX Cal class=

Sagot :

Three of the four towns are on the vertices of the triangle ΔCBD, through

which the bearing can calculated.

Response:

  • The bearing of D from B is approximately 209.05°

Method by which the bearing is found;

From the given information, we have;

AC = AB = 25 km

∠BAC = 90° (definition of angle between north and east)

ΔABC = An isosceles right triangle (definition)

∠ACD = ∠ABC = 45° (base angles of an isosceles right triangle)

[tex]tan(\angle ABD) = \dfrac{45}{25}[/tex]

  • [tex]\angle ABD = arctan \left(\dfrac{45}{25} \right) \approx 60.945^{\circ}[/tex]

The bearing of D from B is the angle measured from the north of B to the

direction of D.

Therefore;

  • The bearing of D from B ≈ 90° + (180° - 60.945°) = 209.05°

Learn more about bearings in mathematics here:

https://brainly.com/question/10710413

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