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# Applied Geometry and Trigonometry

SKMA 103

## Course Description

Prerequisite: Math Level 4. Includes the following geometry topics: angles, triangles, polygons, circles, prisms, cylinders, and cones. Includes right-triangle trigonometry, radian measure, oblique-triangle trigonometry, and graphs of trigonometric functions. May receive credit in only one of the following: SKMA 103, MTH 103, or MT 110. (60-0)

## Outcomes and Objectives

### Define and identify the characteristics of and solve problems related to plane figures (angles, parallel lines, triangles).

#### Objectives:

• Define basic terminology of angles (acute, right, obtuse, straight, complementary and supplementary angles).
• Measure angles with a protractor.
• Define basic terminology of angles formed by parallel lines cut by a transversal (corresponding alternate interior and exterior angles.)
• Define the characteristics of triangles and their properties (altitude, medians, vertex, and sides).
• Express an understanding of and identify the characteristics of congruent and similar triangles.
• Relate to the work place operations.

### Define and identify the characteristics of and solve problems related to Polygons (triangles, squares, rhombus, rectangles, parallelograms, trapezoids and multi-sided polygons).

#### Objectives:

• Use the proper formula for determining area of polygons (square measure).
• Determine the measure of interior angles by using diagonals.
• Relate to the work place operations.

### Define and identify the characteristics of right, isosceles, equilateral and 30? - 60? - 90? triangles.

#### Objectives:

• Know and apply the Pythagorean Formula in solving right triangle problems.
• Solve problems involving similar triangles (tapers).

### Define and identify the characteristics of a circle (chords, central angles, inscribed, segments and sectors).

#### Objectives:

• Demonstrate the relationships between the diameter, radius, and circumference of a circle (? value).
• Solve problems involving area of circles, sectors, and segments.
• Determine arc lengths by using proportions.

### Define and identify the characteristics of an eclipse (enter, major and minor axes).

#### Objectives:

• Solve problems involving area and circumference of an eclipse.
• Express uses of eclipses in everyday situations (orbits, racetracks, buildings, and cutting pipes).

### Define and identify the characteristics of geometric solids (prisms, cylinders, pyramids, cones, frustrums, spheres, torus, prisimatoids).

#### Objectives:

• Use proper formulas to determine surface area of all geometric solids.
• Use proper formulas to determine volume of all geometric solids.
• Figure a cost factor with respect to volume and materials (surface area) of various geometric solids (cylinders, cones, spheres, cubicle containers).
• Relate to the work place operations.

### Define and apply the six trigonometric ratios.

#### Objectives:

• Express the relationship between the sides of a right triangle and the six trigonometric ratios.
• Evaluate the six trigonometric ratios and their inverses with a calculator.
• Apply the six trigonometric ratios to right triangle problems.
• Relate to the work place operations.

### Solve oblique triangles.

#### Objectives:

• Solve oblique triangles using the Law of Sines.
• Solve oblique triangles using the Law of Cosines.
• Relate to the work place operations.