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Head First 2D Geometry by Dawn Griffiths, Stray

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4
10
circles
An arc is a section of the circumference
Covering part of the pizza crust with pepperoni creates an arc. That’s
geometry jargon for a section of the circumference of a circle—whether
it goes almost all the way around a circle, or just a tiny part of it.
Arcs can be described by the proportion of the circumference they
cover—a semicircle covers half—or by the angle of the corresponding
sector (the arc is the outside curved part of the sector).
I describe myself
as “four tenths
of a circle.”
I think of myself as
a 170 degree arc.
Sometimes arcs are described
as fractions. If you only
know the arc angle, then
you have to work out the
fraction.
144º
170º
144
360
=
o
Arc length is circumference x sector angle / 360
To find the length of an arc, first you need to find the circumference of
the circle the arc is part of. That means that you need either the diameter
or radius of the circle. Then you can use the sector angle to find out the
length of the part of the circumference that your arc covers.
Arc Length = 2
π
r × Sector Angle
360°
This calculation helps you find the
fraction of the circle that the
sector represents. If you already
know it’s 2/5 or 1/12, then just use
the fraction instead!
you are here 4 221

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