# Trigonometry – Labeling Triangles

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Triangles are a key feature of the Architecture of Buildings.

Here is a building which contains many triangles.

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The building is in Eindhove Holland and is called ‘De Blob’.

It forms the Admirant Building Entrance.

The Admirant Building is a concrete structure of five storeys, surrounded by the skin of the bubble.

The bubble is made almost entirely of thick glass, held in place by many triangles attached to a complex steel structure .

The Bubble also contains two tunnel entrances, which lead to an underground parking area for about 1,700 bikes.

Triangles are used a lot in Architecture, but not usually in such spectacular from as in ‘De Blob’.

The usual use for triangles involves creating frames which make buildings rigid and strong.

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“Trigonometry” is a branch of mathematics which deals with measuring the sides and angles in Right Angled Triangles.

Architects use Trigonometry to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light.

Trigonometry allows architects to figure out measurements and angles so that their blueprints can be turned into real world structures from raw materials such as steel, wood, and concrete.

It is essential when designing a building to predetermine the geometrical patterns and how much material and labor will be required in order to erect the structure.

Thanks to Trigonometry, when the building is erected, it will be strong with accurate measurements and a budgeted dollar cost.

Definition of Trigonometry

The “Trigon” part of “Trigonometry” refers to a three sided geometrical shape, eg. a Triangle.

Trigon = 3 sides, Hexagon = 6 sides, Octagon = 8 sides, etc.

The “metry” part of “Trigonometry” refers to the activity of measuring.

So the word “Trigonometry” means measurements of the sides and angles in Triangles.

The full story on Trigonometry actually extends beyond Triangles:

Trigonometry is a branch of mathematics which deals with triangles, circles, waves and oscillations.

However, we will only be looking at Triangles in this particular lesson.

Trigonometry and Right Angled Triangles

The Trigonometry we will be covering in this lesson only applies to 90 degree Right Angled Triangles.

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There is a standard way of labeling the angles and sides of a Right Triangle for Trigonometry.

Labeling Angles

Labeling The standard “reference angle” in a Right Triangle is shown below.

The Right Triangle has been drawn in standard position, which means that the “Reference Angle” (or slope angle) is at the bottom left, and the right angle is at the bottom right of the triangle.

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Labeling Sides

The three sides of the Right Angled Triangle are labelled as “Hypotenuse”, “Opposite”, and “Adjacent”.

The “Hypotenuse” is the longest sloping side of the Triangle, just as it is in the “Pythagoras Theorem”.

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The “Opposite” is the side that is directly across from the slope angle.

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The “Adjacent” is the side that is closest to the slope angle.

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When the Triangle is drawn in standard position, its full labeling for use in Trigonometry looks like this:

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The angle “theta” at the bottom of the Triangle is called the standard Reference Angle.

We can also label the Triangle in the same way for the other angle at the top of the Triangle.

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The following five minute video goes through how to Label the Sides of a Triangle for using in Trigonometry.

It covers triangles drawn in all positions, as well as the basic standard position.

Here is another shorter video which shows how to label for both angles in the Triangle:

Labelling Sides Worksheets

This first worksheet labels sides using letters on the Triangle, and has Answers on Page 2 of the sheet.

Labeling Sides Worksheet 1

This second worksheet involves labelling sides using the numerical measurements which are on them, with Answers on Page 2 of the sheet

Labeling Sides Worksheet 2

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