essay 2-3 pages Cost & Estimating
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CSMT 441
Plane Geometry and
Trigonometry
Lecture 4
Plane Geometry
• Point
– A point is a position. It has no length,
width or height.
• Line
– A line connects points.
– The shortest distance between two points is
a straight line.
– A line which has no straight portions is
considered curved.
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Plane Geometry
• Angle
– An angle is formed by two straight lines that
intersect at a point.
– A right angle is 90˚.
– A straight angle is 180˚.
– An angle greater than 90˚ is obtuse.
– Two angles that add together to total 90˚ is said
to be complementary.
– Two angles that add together to total 180˚ is said
to be supplementary.
– If two parallel lines cut by a transverse line the
interior angles are equal. 3
Plane Geometry
• Angles
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Plane Geometry
5
A right angle is neither
obtuse nor acute.
Adjacent and opposite
angles are two or more
angles together.
Plane Geometry
6
Note that the combined angles of the triangle
are equal to 180 degrees, not 360 degrees.
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Plane Geometry
7
Understanding triangles is
extremely important for
pipefitters and workers in
numerous other
construction arena like
estimating.
Plane Geometry
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• Circle
– Tangent
– Radius
– Diameter
– Chord
– Arc
– Circumference
– Sector
– Area ( area of sector)
– Volume of a cylinder; sphere
– Angle in a circle (formed by two radii)
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Plane Geometry
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• Polygon : sum of interior angles = n(n-2)180
where n is number of sides
– A triangle is a 3-sided polygon.
– A quadrilateral is a 4-sided polygon; include:, rhombus,
parallelograms, rectangles, squares, trapezoids, etc
• Areas and perimeters
– The sum of the exterior angles of a polygon is 360˚.
– Pythagorean’s Theorem
• The square of the hypotenuse (longest side of a triangle) of a right
triangle equals the sum of the squares of the legs
Trigonometry
10
• Dealing with the relations of the sides and angles
of triangles and with the relevant functions of any
angles.
• Right Angle Trigonometry (Trigonometric Ratios)
– Right triangles have one angle that is 90˚.
– The Pythagorean Theorem only works if a right angle
exists.
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Trigonometry
11
• Oblique Angles (law of sines and cosines)
– No angles in an oblique triangle are equal to 90˚.
– The oblique triangle can only be calculated if at least
one distance and any two other parts are known. The
other two parts can be either the other two sides, or
any two of the angles, or any combination of the
angles and sides.
– The law of sines is used if an angle and its opposite
side are known in addition to one other side or one
other angle.
– The law of cosines is used if two sides and the
included angle are known.
Trigonometry
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• Oblique Angle Trigonometry