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

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Note that the combined angles of the triangle

are equal to 180 degrees, not 360 degrees.

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Plane Geometry

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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

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• 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

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• 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