# Further trigonometry and four point method

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Further Trigonometry

1.

Composite Figures

A diagram consisting of more than one triangle is said to be a composite figure.

For trigonometric problems involving a composite figure, first decide whether to use sine, cosine or tangent, and then calculate the required length or angle.

Example 1

In the given diagram, find:

a. x

b. y

Solution:

Using a Construction Line

To solve some trigonometric problems, we need to convert the given triangle into two right-angled triangles by drawing a perpendicular construction line from the vertex to the opposite side.

Example 2

Find BC in the given diagram, rounded to 2 decimal places.

Solution:

Draw BD perpendicular to AC. Let BD = x cm, BC = y cm.

2. Directions and Bearings

The direction to a point is stated as the number of degrees east or west of north or south.

For example, the direction of A from O is N30ºE.

B is N60ºW from O.

C is S70ºE from O.

D is S80ºW from O.

Note:

N30ºE means the direction is 30º east of north.

The bearing to a point is the angle measured in a clockwise direction from the north line.

For example, the bearing of P from O is 065º.

The bearing of Q from O is 300º.

Note:

The direction of P from O is N65ºE.

The direction of Q from O is N60ºW.

A bearing is used to represent the direction of one point relative to another point.

For example, the bearing of A from B is 065º.

The bearing of B from A is 245º.

Note:

• Three ...

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