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Trigonometric Ratios – Identify Hypotenuse, Adjacent, & Opposite Sides

Trigonometry is one of the most important branches in Maths. Its been around for a long time. The first uses of Trigonometry go back 3000 years to the Babylonian and Egyptian times. Astronomy played an important part in the lives of ancient cultures and it was Trigonometry that helped the astrological calculations. The word “trigonometry” comes from two ancient Greek word: “trigon”, meaning triangle, and “metron”, meaning measurement. That gives us a clue to what Trigonometry is about. Trigonometry is the study of the relationship between the lengths of a side of a triangle and the angles of a triangle. Before the “Electronic Age”, Trigonometry played an important part in the navigation of ships and exploration of continents to create maps. Trigonometry is still used today in surveying, navigation, engineering, and most sciences.

We’re going to start our study of Trigonometry with right angled triangles. We’ll begin by giving names to the sides and angles of any right angled triangle. Normally, the angles of a triangle are named with capital letters. For example, in the triangle we’ve drawn here. We’ve put the angles A, B, and C. The sides of the triangle and their lengths are labeled with lowercase letters. Here, the side opposite angled “A” is labeled with a small “a” and has a length “a”. The side opposite angle “B” is labeled with a small “b”. Can you see what name we will give to the side opposite angle “C”? Did you say small “c”?

Now I’ve already mentioned that we’re going to begin our work on Trigonometry with right angled triangles. In this triangle ABC, which angle would you say is the right angle? Did you say angle C? Lets mark it as a right angle by creating a small square in the corner. Remember whenever you see the square in the corner, you’ll know that the angle is a right angle. And if there’s no square in the corner, you can’t assume it’s a right angle. Even if it looks like one, it could be 89 or 91 degrees instead of 90.

When we use right angled triangles in Trigonometry we give the sides special names. You would’ve met one of this terms when working with Pythagoras’ theorem. Do you remember what we call the longest side? Did you say the hypotenuse? In this triangle, the side opposite angle C, which is small “c”, is the hypotenuse. Next I’m going to name the other two sides according to the angle I choose. For example, if I choose angle B then the side labeled small “b” is called the opposite side. Opposite should be easy to remember because it’s directly opposite the angle. There’s only one more side remaining. Can you see that this side lays besides angle B? Now the word meaning “lays beside” is adjacent, and that’s what we’re going to call this side. So we have three names for the sides of the triangle.

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