Algebra & Trig, Sullivan & Sullivan
Fourth Edition
Notes:§8.4
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§8.4 – Area of a Triangle
Practice finding the area of a triangle: SAS triangles
A
1
 c  a  cos 
2
(for any two sides a & c, and the angle β between them)
Finding the area of a triangle: SAS triangles
A
1
 base  height
2
However, what if we're given a SAS tri?
We'll need to figure out what height is:
If we're given a, c, and β (on the picture to the right), by definition cos   
Solving for h, we get
a  cos   h
Plugging that back into the original, we get
A
h
a
1
 c  a  cos 
2
Given any two sides, and the angle between them, this reasoning will hold, and thus we can use the same formula
Practice finding the area of a triangle: SSS triangles
A  ss  a s  bs  c 
<Proof is beyond the scope of this lesson>
s
1
a  b  c 
2