BEARINGS

CONTENT

1. Revision of;

(i) Trigonometric ratios;

(ii) Angles of elevation and depression.

2. Notation for bearings: (i) Cardinal notations N30⁰E (ii) S45⁰W

3. 3-digits notation. E.g. 075⁰, 350⁰.

4. Practical problems on bearing.

REVISION OF TRIGONOMETRIC RATIOS

Parts of a Right-angled Triangle

The hypotenuse will always be the longest side, and opposite from the right angle.

(Imagine that you are at Angle A looking into the triangle.)

The adjacent side is the side next to Angle A. It’s that sides that has angle 90 and unknown angle on it.(The opposite side is the side that is on the opposite side of the triangle from Angle A.)

Opposite side is the side facing the unknown angle

The ratios are still the same as before!!

\(Sin A = \frac{\text{opposite }}{\text{hypotenuse}} = \frac{a}{c} \\ Cos A = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{b}{c} \\ Tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{a}{b} \\ Cosec A = \frac{1}{sinA} = \frac{\text{hypotenuse}}{\text{opposite}} = \frac{c}{a} \\ Sec A = \frac{1}{cosA} = \frac{\text{hypotenuse}}{\text{adjacent}} = \frac{c}{b} \\ Cot A = \frac{1}{tanA} = \frac{\text{opposite}}{\text{adjacent}} = \frac{b}{a} \)

Examples

1.