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This is a Clilstore unit. You can link all words to dictionaries.

SOLVING TRIANGLES (2) - TRIGONOMETRY

INTRODUCTION

What do you know about Trigonometry? Where was it first used and why? Can you imagine the huge revolution it involved?

Trigonometry is a word derived from Greek that means trigōnon, "triangle", and metron, "measure".

Let's learn more about it watching this video. You can use the transcription given in Activity 1 and you must fill in the gaps.

SOLVING TRIANGLES: LAW OF SINE AND LAW OF COSINE

A triangle has six parts, three sides and three angles. Given almost any three of them—three sides, two sides and an angle, or one side and two angles—you can find the other three values. This is called solving the triangle, and you can do it with any triangle, not just a right triangle.

For all of this, you need only two tools, the Law of Sines and the Law of Cosines. The Law of Sines relates any two sides and the angles opposite them, and the Law of Cosines relates all three sides and one angle.

In the webs listed you can learn more about these two laws and review some examples.

- Solving triangles (Mathisfun)

- Trigonometry with geneal triangles (Khanacademy)

- Law of sines (Mathwarehouse)

 After that, go to Activity 2 and solve the problems suggested. Share your answers with the teacher.

TRIGONOMETRY IN REAL LIFE!

Science, navigation and surveying are only some of the original applications of Trigonometry. Nowdays, Trigonometry and its functions have an enormous number of uses in our daily life. For instance, Trigonometry is applicable in various fields like satellite navigation, chemistry number theory, medical imaging, electronics, electrical engineering, civil engineering, architecture, mechanical engineering, oceanography, seismology, phonetics, image compression... and even computer music or game development!!

Do you want to discover more? Watch this video about real and present applications of Trigonometry: 

You can also have a look to this insteresting site: Applications of Trigonometry

Now, in groups of five, share you reflections and prepare a short oral presentation about Trigonometry in real life. The work will be presented to the whole class during the next day. In Activity 3 you will find very useful tips to give an oral presentation.

MEASURING DISTANCES

Activity 4: Choose three international cities. Using Google Earth, research two of the distances between the cities and the angle between those two paths. And calculate the distance between the other two cities. What Law do you need and why? Send your answer to the theacher.

CLOSURE 

In this lesson we've learnt Law of Sines and Law of Cosines, that allow you to solve any kind of triangle, not only right-triangles. 

It's true that triangles are one of the simplest geometrical figures, but they have varied applications. As we learnt in the initial video, the primary application of Trigonometry was found in India and Greece when precise distances needed to be measured. In our daily life, Trigonometry has more applications than we have ever imagined!

So, we can state Mathematics is a subject that is vital for gaining a better perspective on events and applications that occur in the natural world. 

Clilstore ACTIVITY 1ACTIVITY 2ACTIVITY 3CONCEP MAP

Short url:   https://clilstore.eu/cs/4885