C2 Sine and Cosine rules

Sine and cosine notes including the ambiguous case and past paper examples

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  • Created on: 30-04-11 13:35
Preview of C2 Sine and Cosine rules

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C2 the sine and cosine rules.
If you know one side, the opposite angle and one other value use the sine rule.
If you know all 3 sides use the cosine rule.
If you know 2 sides and the angle between them use the cosine rule.
The ambiguous case
Two angles between 0 and 180 degrees can have the same sine.
This means two different triangles with different areas can be drawn from
the same information.
In general if x= y degrees then x also equals 180 ­ y.
These questions will ask for values rather than value.
WJEC C2 May 09 qu3.
The triangle ABC is such that AB = 16 cm, AC = 9 cm and ABC = 23°.
(a) Find the possible values of ACB. Give your answers correct to the nearest degree. [2]
=44,136 degrees
(b) Given that BAC is an acute angle, find
(i) the size of BAC, giving your answer correct to the nearest degree,
18013623= 21 degrees
(ii) the area of triangle ABC, giving your answer correct to one decimal place. [4]
Using the cosine rule for sides:
a^2=9^2+16^22*9*16Cos 21
a =8.25
=25.8 cm^2 1dp


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