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 Side 2. The Tangent Ratio

 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.

longest side hypotenuse  The longest side of a right-angled triangle is called the hypotenuse.  It is always opposite the right position with respect to a specific angle  The other two sides of a right-angled triangle are named according to their position with respect to a specific angle. opposite to opposite  The side which is opposite to the angle is named opposite next to adjacent  The side next to the angle is named adjacent.

 In the diagram the longest side, opposite the right angle, is side AB. AB hypotenuse  So AB is the hypotenuse.  Side BC is opposite angle θ and side AC is next to angle θ.  So, in relation to this BC opposite angle, side BC is ‘opposite’ AC adjacent and side AC is ‘adjacent’.

 In trigonometry, the ratios of sides in right- angled triangles are of particular importance.  These ratios have special names. ratio opposite side to the adjacent side tangent ratio  In any right-angled triangle, the ratio of the opposite side to the adjacent side is called the tangent ratio.

 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.