Transcript 10.5 Trigonometry and Area

10.5 Trigonometry and Area
Additional Formula for Area of
Triangles (Using Trig)
The c*sin(A) portion of this formula will provide you with the
height from B to AC.
10.6 Circles and Arcs
Important Vocabulary
• Circle – Set of all points in a plane that are
equidistant from a given point called the center
• Diameter – a segment that contains the center of
a circle and has both endpoints on the circle.
• Radius – a segment that has one endpoint at the
center and the other endpoint on the circle.
• Congruent Circles – circles with congruent radii
• Central Angle – an angle whose vertex is the
center of the circle.
• There are several different central angles that
we could talk about in this picture. The sum
of all adjacent non-overlapping central angles
is 360 degrees.
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Arc – a part of a circle.
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Semicircle – half of a circle  180
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Minor Arc – any arc smaller than a semicircle  180
Major Arc – any arc greater than a semicircle.  180o
• A minor arc is named by its endpoints.
• A major arc (and semicircle) is named by its
endpoints along with a third point on the arc (the
third point is the middle letter and is used as a set of
directions for tracing out the appropriate arc)
Adjacent arcs – arcs of the same circle that have
exactly one point in common.
This concept parallels the idea of segment addition and angle addition.
• Circumference – the distance around the
circle. The number pi (  ) is the ratio of the
circumference of a circle to its diameter.
• Regardless of how large your circle is, if you
were to measure the circles circumference
and diameter then divide the two of them in
the order of circumference/diameter every
single time your answer will be pi.
All circles are similar to one another.
• Concentric circles – coplanar circles that share
the same center.
• The measure of an arc is in degrees. The arc length
is the fraction of the circumference. Arc length is a
distance.
• The arc length is found by determining what
fraction of 360 degrees your arc is representing.
Then take that fraction and multiply it by the
circumference of the circle.