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Math 10C Module 1 Lesson 7

Module 1: Part 2 Trigonometry

 

 

Glossary Terms

 

Retrieve your handout titled “Glossary Terms” from your binder. Add the following terms:

  • adjacent side

  • cosine ratio

  • hypotenuse

  • opposite side

  • proportional

  • Pythagorean theorem

  • reference angle

  • right triangle

  • sine ratio

  • solving a triangle

  • tangent ratio

NAMING OF SIDES

The three sides of a right triangle are known by three different names. You need to be able to identify the opposite side, the adjacent side, and the hypotenuse.

 

The term hypotenuse may already be familiar to you. Have a look at the diagrams where the orange arrows each point to the hypotenuse. Can you see a pattern? If you were given a right triangle, how could you identify the hypotenuse?

 

This graphic shows an illustration of three right triangles. Each right triangle has an arrow pointing to its hypotenuse.

 

The great thing about the hypotenuse is that it never changes locations—it is always directly across from the right angle.
Did you discover that pattern when you viewed the diagrams?

 

The two other sides that you need to identify are the opposite side and the adjacent side. The location of these other two sides will change, depending on which angle is being considered in the question.

 

This graphic shows an illustration of a right triangle with acute angle x.

 

 

 

For example, if you had the triangle to the right, you can see that the angle we need to find is labelled x. So, in this case, x is the reference angle. Can you tell which side is opposite from angle x?

 

This graphic shows a right triangle with an arrow pointing to the bottom side, opposite angle x.

 

 

If you said the bottom, you are correct!

 

See how the bottom side is opposite (or directly across) from angle x? In this case, we would label the bottom as the opposite side.

 




This shows an illustration of a right triangle with acute angle y.

 

 

 

What about in the case to the left? Can you identify the opposite side if you are using angle y as the reference angle?

 

This graphic shows a right triangle with an arrow pointing to the left side, opposite angle y.

In this case, the left side is opposite from the reference angle.

 




Now that you can label the hypotenuse and the opposite side of a right triangle, all you need to do is label the remaining side as the adjacent side. You can also think of the adjacent side as the side between the reference angle and the 90° angle. Please review the examples below.

 

This illustration shows a right triangle with an arrow pointing to the left side, opposite angle y.This graphic shows a right triangle with an arrow pointing to the left side, adjacent to angle x.
 

 



Learn and Listen

 

The interactive piece titled “Shape and Space” allows you to practise identifying the sides of a triangle by dragging and dropping the opposite, adjacent, and hypotenuse sides into their correct locations. You can find the interactive piece on the right-hand side of the website.

 

Self-Check

Complete the following self check using the link below to practice identifying the hypotenuse, the opposite side and the adjacent side.: