Lesson 1
1. Lesson 1
Module 1: Trigonometry
Lesson 1: Working with Multiple Triangles
Focus
Trigonometry can be used to determine distances and angles when it is not feasible to measure them directly.
For example, Gerard is a window washer who charges his clients based on the area to be washed. He knows the width of an office tower, but he also needs the height. Although he dressed up as Spiderman at Halloween, he can’t crawl up the outside of buildings. This means that he can’t just use a tape measure to determine the building’s height. He could, however, stand on the roof of an adjacent building and determine the height indirectly using trigonometry.
angle of depression: an angle with one horizontal arm, and one arm below horizontal
angle of elevation:an angle with one horizontal arm and one arm above horizontal
From the top of the adjacent building, Gerard uses a clinometer and determines that the angle of depression to the base of the office tower is 38° and the angle of elevation to the top of the office tower is 52°.
You will be presented with a number of definitions in this lesson. Remember to add any definitions and corresponding diagrams to your Glossary Terms document.
Gerard’s first step would be to draw a diagram. He might draw one like this:
You will notice that the diagram Gerard drew has two right triangles. You might remember from previous math courses that knowledge of trigonometry and the Pythagorean theorem will be helpful in solving problems that involve triangles.
In this lesson you will use the primary trigonometric ratios and the Pythagorean theorem to solve problems involving multiple right triangles.
This lesson will help you answer the following inquiry question:
- How can you use multiple triangles to solve indirect measurement problems?
Important!
Your calculator must be set to degree mode for all calculations done in Mathematics 20-2.
Just like there are different units of measure for distance (e.g., kilometres and centimetres), there are different units of measure for angles (e.g., degrees and radians). And just like you would get an incorrect answer if you used kilometres where centimetres were expected, you will get incorrect answers if you use radians or grads instead of degrees.
Have a look at your calculator screen. Typical calculators will show “Deg,” “Rad,” or “Grad.” If your calculator shows “Deg,” it is in degree mode. If your calculator shows either “Rad” or “Grad,” you need to press the Mode or DRG button until you see “Deg.”
If you cannot determine how to set your calculator to degree mode, you will need your calculator’s manual. These manuals can often be found on the Internet by entering your calculator’s make and model number into a search engine.
Assessment
- Lesson 1 Assignment
This lesson provides you with opportunities to investigate, discuss, and practise the knowledge and skills you are learning. For instance, in Try This and Share, you can check your answers with other students to see if you are on track. If you are having difficulty with concepts or calculations, contact your teacher.
All assessment items you encounter need to be placed in your course folder. You should have already had a discussion with your teacher about which items you will be handing in for marking. Make sure you follow your teacher’s instructions.
Save a copy of the Lesson 1 Assignment to your course folder. You will receive more information about how to complete the assignment later in this lesson.
Time
Each module is made up of lessons. Each lesson in Mathematics 20-2 is designed to be completed in approximately 80 minutes. You may find that you require more or less time to complete different lessons depending on your strengths. It is important that you progress at your own pace based on your individual learning requirements.