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- 10 week duration
Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.
An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.
Trigonometry with Right Triangles
Here we focus on right angle triangles within quadrant I of an x-y plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.
Trigonometry with Oblique Triangles
This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.
Introduction to Algebra
Functions and Graphs
This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.
- Identify, measure, and calculate different types of straight lines and angles
- Calculate the interior angles of polygons
- Solve problems involving a variety of different types of triangles
- Calculate the area of a variety of different types of quadrilaterals
- Solve problems involving circles
- Calculate the areas and volumes of different solids
Introduction to Statistics
Problem Solving with Trigonometric Functions
Many application problems involving right triangles use words like angle of depression and angle of elevation. The angle of depression is angle measured below the horizontal, and may also be called the angle of declination. The angle of elevation is the angle measured above the horizontal (see figure below), and may also be called the angle of inclination.
Let’s start with a couple of basic angle of elevation problems:
The next example is a little more complex than the ones shown above, since it involves working with more than one right triangle and it’s an angle of depression problem. See if you can solve the question on your own before viewing its solution:
Finally, not all trigonometric ratio problems you encounter will be angle of elevation or depression-based. Here’s an example involving two right triangles facing one another.
Now that you’ve seen several examples, try answering the questions underneath. Post your solutions in the comments section.
To find the height of a flagpole (shown below), a person measures 35.0 ft from the base of the pole and then measures an angle of 40.8° from a point 6.00 ft above the ground to the top of the pole. Find the height of the flagpole.
After leaving port, a ship holds a course N 46° 12′ E for 225 M (nautical miles). Find how far north and how far east of the port the ship is now located.
Source: Technical Mathematics with Calculus, 3e. Calter & Calter.