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The Law of Sine and Cosine

The equations and examples for law of sine and cosine!
by

lauren curlee

on 22 May 2015

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Transcript of The Law of Sine and Cosine

The Laws of Sine and Cosine
Lauren Curlee and Matilda Chidlaw
The Law of Sine
When to use:
Use any 2 fractions
Must have side and angle opposite
Use with NON-right triangles
a
A
b
B
c
C
Ambiguous Case: Law of Sines
Given: Angle, Side, Side
ASS
Example
Example of How to use Law of Sine:
Given:
m < C = 30
ac = 7
cb = 6
The Law of Cosine
When to Use:
Always need 2 sides and the angle they form!
Example of Law of Cosine
c
a
b
B
A
C
30
o
c
A
B
7
6
angle
side
side
7
_____
sin(B)
=
6

____
sin(30)
sin(B) = 7(sin(30))
____
6
That comes out to: m<B = 36
o
But because you were given angle, side, side you need to account for the 2 possible triangles since angle B could change.
30
7
6
* still same triangle according to given information, but angle B has changed.
How to account for 2
nd
triangle
You need to make angle B obtuse, which means you need to take the angle you found before (36) and subtract it from 180.
Now the angles you have are <A = 30 and the new <B, or B' = 144. These angles added together equal 174, which is less than 180.
This means that it is an ambiguous case and the value for C' = 6.

If you were a given a triangle like this and asked to solve you would need to account for both triangles.

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