In Mathematics, the study of bearings enables us to tell the position of objects with reference to o

Question

In Mathematics, the study of bearings enables us to tell the position of objects with reference to one another.
Two important things about bearing:
• Angle (in degree), measured clockwise from the north direction.
• Must always be stated in three digits. with $000^\circ\leq\theta<360^\circ$
Let’s look at the diagram below.

Find the bearing of $B$ from $A$.

Join $A$ and $B$.
Construct $N$ at reference point $A$.
Measure angle clockwise from $N$ of reference point $A$.

The bearing of $B$ from $A$ is $035{}^\circ$.

Find the bearing of $A$ from $B$.

Join $A$ and $B$.
Construct $N$ at reference point $B$.
Measure angle clockwise from $N$ of reference point $B$.

The bearing of $A$ from $B$ is $215{}^\circ$.

Bearing of $A$ from $B$ is not the same as the bearing of $B$ from $A$.

The following are $3$ angle properties involving straight line:
• Alternate angle
• Corresponding angle
• Interior angle
are used quite often to find the bearings.
Know the directions
Problem involving Bearings
May involve the use of Sine Rule
• Sine Rule
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$ used when there are two given sides and one non-included angle, or when they are two given angles and one given side.
• Cosine Rule
$c^2 = a^2 + b^2 - 2ab \cos C$ used when there are two given sides and one included angle, or when all three sides are given.

Accepted Answer

Bearings are measured clockwise from north and written using three digits. In the example, the bearing of $B$ from $A$ is $035^\circ$, while the bearing of $A$ from $B$ is $215^\circ$.

Bearings

Bearings

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