Question

Matilda walks from a castle's tower to its drawbridge by heading 624 m due

east and then heading due south.
The straight-line distance from the tower to the drawbridge is 927 m.
Work out the bearing of the drawbridge from the tower.
Give your answer to the nearest degree.

Answer 1

138° (nearest degree)

Explanation:

Bearing: The angle (in degrees) measured clockwise from north.

The given scenario can be modelled as a right triangle (see attachment).

Therefore, the bearing is 90° + θ (shown in green on the attached diagram).

To find angle θ, use the cosine trigonometric ratio:

`\implies cos(\theta)=(A)/(H)`

`\implies cos(\theta)=(624)/(927)`

`\implies \theta=\cos^(-1)\left((624)/(927)\right)`

`\implies \theta=47.69018863...`

`\implies \theta=48^(\circ)\; \; \sf (nearest\;degree)`

Therefore, the bearing of the drawbridge from the tower is:

`\begin{aligned}\implies \sf Bearing&=90^(\circ)+\theta\\&=90^(\circ)+48^(\circ)\\&=138^(\circ) \end{aligned}`

Answer 2

• The bearing of the drawbridge from the tower is 138° SE

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The segments that are formed by Matilda walking from the tower to drawbridge form a right triangle

• Horizontal leg = 624 m,
• Hypotenuse = 927 m.

Find the angle x between the two segments

• cosine = adjacent / hypotenuse
• cos x = 624/927
• x = arccos (624/927)
• x = 48° (rounded to the whole degree)

Find the bearing of the drawbridge from the tower

Add 90° to the angle measure we just found, since bearing is counted from the north direction:

• 48° + 90° = 138° SE