Teacher Note: Trigonometry will be discussed in this lesson and should not be used as an introduction to a unit on Trigonometry. Students will need a basic understanding of Trigonometry to complete the tasks in this lesson.
Learning Outcomes
The students will:
- Demonstrate an understanding of trigonometric ratios by solving a problem involving a right triangle.
CONNECT
Goals:
The students will:
- Choose, then apply the trigonometric ratio to calculate the height of a triangle given the other two sides.
Task:
Students generate word problems using pictures, words, and symbols relating to a video example.
Activate Prior Knowledge:
- View drawings of Pacific Northwest Basket Traps.
- Watch the following video on the Ktunaxa Fish Trap.
Reminder: It is important to stop throughout the story and give students (A/B partners) opportunity to talk or respond to the story.
- Ask students if they can use their knowledge of trigonometry to find the height of the fishtrap. (Round to the nearest tenth of a centimetre and to the nearest degree.)
- Prior knowledge needed:
- the three trigonometric ratios: sine, cosine, tangent
- the knowledge required to 'solve triangles' as stated in the IRP.
- For their answer to be complete, they need to:
- Draw a triangle with labelled parts to match the problem.
- Write an equation.
- Solve the equation.
- Write a sentence to answer the problem.
Videos
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Click above to view video in Mac OSX (Quicktime)
(Video Length: 3 mins)
Click above to view video in Windows (Media Player)
(Video Length: 3 mins)
PROCESS
Predict and Question:
Given the previous information, ask the students what is the approximate height of a fishtrap. Students discuss with A/B partners the different height possibilities.
Procedure:
Have the students draw and label a triangle to match the problem.
To find the height, given A, either the tan or cos ratios can be used
Therefore what is the height of the fishtrap?
Therefore what is the height of the fishtrap?
TRANSFORM
Students generate word problems using pictures, words, and symbols relating to the video example. For example, a variety of word problems can be created by using the same formula as above and changing the data.
A/B Partners - Student partner groups trade their word problems with other partner groups and solve problems.
REFLECT
When can you use the trigonometric ratios to solve a problem in real application? Use examples in your explanation.
Extend learning or next lesson
Students can find examples of right triangles and right triangle shaped objects in the local community to present to the class. The presentation can take many forms such as collages/videos/ photographs/drawings, etc. Students use the visual connection in order to apply the trigonometric ratios.