anonymous
  • anonymous
a segment of a circle has a 120 degree arc and a chord of 8 to the square root of 3 inches. find the area of the segment.
Geometry
chestercat
  • chestercat
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amistre64
  • amistre64
what does "8 to the square root of 3" mean?
amistre64
  • amistre64
\[8^{(\sqrt 3)}\] ??
anonymous
  • anonymous
\[8\sqrt{3}\] this is what it looks like in the problem

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amistre64
  • amistre64
thats: 8 square roots of 3 then, no "to" required
amistre64
  • amistre64
terminology ... what is a segment?
anonymous
  • anonymous
the part of a figure cut off by a line
amistre64
  • amistre64
so instead of a slice of pizza, its just the crust right?
anonymous
  • anonymous
yes, basically
amistre64
  • amistre64
ok, i get those mixed up alot. so we want the area of the slice, minus the area of the triangle .. any ideas?
amistre64
  • amistre64
|dw:1436478599531:dw|
amistre64
  • amistre64
do we know trig? or special triangles?
anonymous
  • anonymous
no, we do not
amistre64
  • amistre64
well, without trig or some knowledge of special triangles, we really cant approach this.
amistre64
  • amistre64
the special triangle we would need to know about is a 30-60-90 degree
anonymous
  • anonymous
so then how would we apply that to an equation?
amistre64
  • amistre64
if you have formulas at your disposal, then you might be able to use them .. but i do not know what you have available to you. hence my thought to use a 30-60-90 special triangle
amistre64
  • amistre64
|dw:1436478952947:dw|
anonymous
  • anonymous
area of segment=area of sector-area of triangle
amistre64
  • amistre64
ideally we learn, that a 30-60-90 can be constructed from an equilateral triangle, where all the sides are the same length |dw:1436479033334:dw| using the pythagorean thrm, we find that the missing side is sqrt(3) giving us the special ratio of: |dw:1436479105655:dw|
amistre64
  • amistre64
in your case, we can then use it to scale to the desired length |dw:1436479181984:dw|
amistre64
  • amistre64
but if you have no knowledge of this, then i dont see much of a way to approach a solution
amistre64
  • amistre64
|dw:1436479458168:dw| we have 120/360 of the area of the circle (pi 8^2) and we have 2 triangles (a rectangle is 2 triangles) of base 4, and height 8sqrt(3)
amistre64
  • amistre64
height of 4sqrt(3) THAT IS
amistre64
  • amistre64
as i mentioned, without some trig or knowledge of the special 30-60-90 triangle, i see no way to approach this problem ...
anonymous
  • anonymous
okay well thank you for trying

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