# C2 Sine and Cosine rules

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

- Created by: Olivia
- Created on: 30-04-11 13:35

First 202 words of the document:

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]

SinC/16=Sin23/9

=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

1/2abSinC

0.5*8.25*9Sin136

=25.8 cm^2 1dp

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