Using Trigonometry
In this unit, students will explore the use of trigonometry to find unknown sides and angles in right-angled triangles, taking the concepts that were developed in the previous unit Introducing Trig and looking at different ways of practising the new skills. Students will then develop and reinforce skills to solve practical problems in trigonometry using the problem solving model
reality 
model 
solution 
check
It is important that good algebraic skills are used in setting out their work, and students can be encouraged to practice these individually and using cooperative logic problems in a group situation.
label right angled triangles with respect to a given angle
use trigonometric ratios to calculate the length of opposite and adjacent sides in right angled triangles
use trigonometric ratios to calculate the size of angles in right angled triangles
Maths skills required from other strands
algebraic skills for solving equations
rounding
This unit begins with an individual activity designed to reinforce the idea that the ratios determined in a measuring task are the same as those found by using the trigonometric ratios. The students need to measure the angle and label the triangles correctly before measuring the lengths of the sides and determining the ratios.
After demonstrating a suitable method for solving triangles involving how to choose the correct ratio, and how to solve the ensuing equation, students need to practice these skills both individually, and in a group situation using matching card activities and cooperative logic activities. Appropriate rounding needs to be discussed with the students and the reasonableness of answers needs to be looked at.
Applying trigonometry to practical situations is an important aspect of this unit, and suitable practical activities involving the students going outside to take measurements using long measuring tapes and clinometers (measure angles of inclination) will give the students a better understanding of the wide uses of trigonometry.
Getting Started
- Each student needs a triangle worksheet and a recording sheet. To begin this activity the students need to learn how to label right-angled triangles with opp, adj and hyp in relation to a given angle. Once this has been done, a final measuring activity should be completed individually to reinforce the links between the ratios and sin, cos and tan for different angles. Students should measure the angle size and lengths of sides for the ten triangles, and record the results on the recording sheet. They can then calculate the values of sin, cos and tan for each triangle. These results can be added to the three graphs created in the Introducing Trig to check for consistency of the results.
- Students should now be shown the way to use the sin, cos and tan ratios to:
- calculate unknown sides in right angled triangles, given an angle and another side.
- calculate unknown angles in right angles triangles, given two sides of the triangle.
Exploring
- Working in pairs, each pair should be given a set of matching activities. These matching activities can be modified to be used in a variety of ways. The sheets can be cut up and placed in arbitrary order and the students challenged to put them in the correct order. Alternatively the teacher can delete parts of the sheet and the students can be challenged to:
- write symbols to match words
- write words to match symbols
- fill in gaps in the words and symbols
- Working in groups of about 5, each group is given a cooperative logic problem to solve.
- Each person in the group is given one clue card.
- Each person reads out their clue to the rest of the group. (Some problems may have unnecessary information mixed in with facts).
- The group then works on solving the problem cooperatively.
- The solution should be checked by reading the clues again.
Reflection
- Practical problem solving activities
The students can now use their trigonometric ability to challenge each other with practical problems.
Split the class into small groups and get each group to pose a question that could be solved using trigonometry. Encourage them to find practical measuring tasks, where they measure distances, and angles to find the heights of buildings, trees, flagpoles, etc, or the width of streets, etc.
- Get the groups to swap problems and solve each other’s trigonometry questions.
| Attachment | Size |
|---|---|
| UsingTrigonometryCM1.pdf | 51.75 KB |
| UsingTrigonometryCM2.pdf | 48.45 KB |
| UsingTrigonometryCM3.pdf | 116.91 KB |
| UsingTrigonometryCM4.pdf | 67.81 KB |
Similar Resources
Investigating the Idea of Sin
In this unit we explore the sine and related functions to find out specific values, relations between them, and applications.
I'm So Sorry I Ate Chocolate
This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Sine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. Finally we compare the use of the Sine Rule and the Cosine Rule.
Note that this unit may contain more material than you need for some classes. You may want to choose only some of the sessions if you have not planned to allot five sessions on the Sine Rule and its relation to the Cosine Rule.
Trigonometric Applications Outside the Classroom
This unit follows on from others that introduce students to sine, cosine and tangent. In this unit students will gain practical experience in using trigonometry in practical situations; mainly outside the classroom.
Introducing Trig
In this unit students will explore the importance of triangles, particularly right angled triangles, in the real world. Students will use practical measuring skills and calculations to find a pattern linking the ratio of the sides of a triangle with the angles.
This unit may take longer than one week, but introducing trigonometry using scale diagrams and practical measuring tasks allows for improved understanding of the concepts and how they apply to real life situations.
Cosine Rule
This unit explores the magnitudes of sides and angles of a triangle and leads to the discovery and proof of the Cosine Rule. This Rule is then used to solve triangles, some of which arise in practical situations. We note that the Cosine Rule is a generalisation of Pythagoras’ Theorem.
Note that this unit may contain more material than you need for some classes. You may want to choose from parts of this unit if you have not allotted 5 sessions on the Cosine Rule to your class.
