Question

A, B, C and D are four towns.

Answer 1

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)

$tan(\angle ABD) = \dfrac{45}{25}$

• $\angle ABD = arctan \left(\dfrac{45}{25} \right) \approx 60.945^{\circ}$

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:

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