trigonometry – right angled triangles by the end of this lesson you will be able to identify and...
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Naming the sides of a right-angled triangle
Trigonometry – Right Angled Triangles
By the end of this lesson you will be able to identify and calculate the following:1. Hypotenuse, Opposite Side, and, Adjacent Side2. The Tangent Ratio
Naming the sides of a right-angled triangle:
In trigonometry, angles are often named using letters of the Greek alphabet, such as: θ (pronounced as ‘theta’), α (pronounced ‘alpha’), β (‘beta’), γ (’gamma’) and others.
Naming the sides of a right-angled triangle:
The longest side of a right-angled triangle is called the hypotenuse. It is always opposite the right
The other two sides of a right-angled triangle are named according to their position with respect to a specific angle.
The side which is opposite to the angle is named opposite
The side next to the angle is named adjacent.
Naming the sides of a right-angled triangle:
In the diagram the longest side, opposite the right angle, is side AB.
So AB is the hypotenuse.
Side BC is opposite angle θ and side AC is next to angle θ.
So, in relation to this angle, side BC is ‘opposite’ and side AC is ‘adjacent’.
Worked Example:
Worked Example
The Tangent Ratio:
In trigonometry, the ratios of sides in right-angled triangles are of particular importance.
These ratios have special names.
In any right-angled triangle, the ratio of the opposite side to the adjacent side is called the tangent ratio.
Worked Example
Worked Example
From the previous worked example we can conclude that: regardless of size any right-angled triangle
where one of the angles is equal to 30°
the ratio of the side opposite that angle to the side adjacent to that angle (the tangent ratio) will always be 0.58.
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