Learning Goals
- Recognise the connections between similarity and the trigonometric ratios. (ACMMG223)
- Use Pythagoras’ Theorem and trigonometry to find unknown sides of right-angled triangles. (ACMMG222, ACMMG224)
Timeframe: 8 lessons
Introduction
TASK 1
Watch the following videos.
SINE
How do you find the sine of an angle in a right angle triangle?
How do you find the missing side of a right angle triangle using sine?
COSINE
How do you find the cosine of an angle in a right angle triangle?
How do you find the missing side of a right angle triangle using cosine?
TANGENT
How do you find the tangent of an angle in a right angle triangle?
How do you find the missing side of a right angle triangle using tangent?
Watch the following videos.
SINE
COSINE
TANGENT
Exploration
TASK 2
1. In pairs, draw a large right-angled triangle on graph paper and accurately measure and label the angles and side lengths.
2. Use the poster below to see if the trigonometry short-cuts on the poster below work for your triangle. Show another group and/or Mr Flynn how it works.
1. In pairs, draw a large right-angled triangle on graph paper and accurately measure and label the angles and side lengths.
2. Use the poster below to see if the trigonometry short-cuts on the poster below work for your triangle. Show another group and/or Mr Flynn how it works.
Assignment
TASK 3
Watch the Catalyst video about Applying Trigonometry: Leaning Tower and answer the following questions.
Website: http://splash.abc.net.au/media/-/m/154926/applying-trigonometry-leaning-tower
1. Listen for the dimensions of the tower. What is its height and at what angle is it leaning?
Height:
Angle:
2. Draw the triangle made between the tower, the ground and the falling object.
3. How far from the tower should the melons hit the ground? Use a trigonometric ratio to work out the distance to the nearest centimetre (show working).
4. Design a tower where the dropped object will fall exactly 100 m vertically and land exactly 10m from the base of the tower. Include all measurements and angles.
TASK 4
Some Video / Animation Options:
Discuss with Mr Flynn which topic you are going to create a tutorial for:
Watch the Catalyst video about Applying Trigonometry: Leaning Tower and answer the following questions.
Website: http://splash.abc.net.au/media/-/m/154926/applying-trigonometry-leaning-tower
1. Listen for the dimensions of the tower. What is its height and at what angle is it leaning?
Height:
Angle:
2. Draw the triangle made between the tower, the ground and the falling object.
3. How far from the tower should the melons hit the ground? Use a trigonometric ratio to work out the distance to the nearest centimetre (show working).
4. Design a tower where the dropped object will fall exactly 100 m vertically and land exactly 10m from the base of the tower. Include all measurements and angles.
TASK 4
"Teach Me Trig!" Animation / Video Tutorial
Learning Goal: Apply trigonometry to solve right-angled triangle problems(ACMMG224)
Task: With a partner complete the following two (2) parts:
Examples:
Learning Goal: Apply trigonometry to solve right-angled triangle problems(ACMMG224)
Task: With a partner complete the following two (2) parts:
- Create a video or animation to explain how to use a trigonometric ratio to find an unknown side or angle in a right-angled triangle
- Create a real-life application ‘maths problem’ that would check to see if a person has understood your tutorial. Write the problem on one piece of paper and the solution (show all working out) on another piece of paper. Staple the papers together and submit.
- Watch some of the videos in the Introduction to this unit.
- If you’re stuck, look in your textbook to get some ideas for your real-life problems that use trigonometry to find a solution
- Video – use your phone, iPod, iPad or tablet to record a ‘live’ explanation (similar to theVirtual Nerd tutorials).
- iPad Apps – EduCreations, Doceri, Show Me, Do Ink, Toontastic
- Laptop / Desktop – animate a presentation then record a voiceover (PowerPoint,Keynote), Powtoon, GoAnimate
Discuss with Mr Flynn which topic you are going to create a tutorial for:
- Sine Ratio - Find Unknown Opposite Side
- Sine Ratio - Find Unknown Hypotenuse
- Sine Ratio - Find Unknown Angle
- Cosine - Find Unknown Adjacent Side
- Cosine - Find Unknown Hypotenuse
- Cosine - Find Unknown Angle
- Tangent Ratio - Find Unknown Opposite Side
- Tangent Ratio - Find Unknown Adjacent Side
- Tangent Ratio - Find Unknown Angle
Skills
TASK 5
Complete the following activity booklets:
TASK 6
Login to Mathletics and complete the following four lessons in MG - Pythagoras and Trigonometry module:
Complete the following activity booklets:
- Introduction to Trigonometry
- Trigonometric Ratios and Calculator Tricks
- Finding Angles and Sides in Right Angle Triangles
TASK 6
Login to Mathletics and complete the following four lessons in MG - Pythagoras and Trigonometry module:
- Hypotenuse, Adjacent, Opposite
- Sin A
- Cos A
- Tan A
- Find Unknown Sides
- Find Unknown Angles
Review
TASK 7
Add to your Maths Journal what you have learnt in this module.
Use diagrams, pictures, words, symbols and colour to express your learning.
Submit your Maths Journal when completed.
Add to your Maths Journal what you have learnt in this module.
Use diagrams, pictures, words, symbols and colour to express your learning.
Submit your Maths Journal when completed.
No comments:
Post a Comment