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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:
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