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Introduction to the tangent ratio.

 This topic is part of the TCS FREE high school mathematics 'How-to Library'. It introduces the 'tangent ratio' for right angled triangles. (See the index page for a list of all available topics in the library.) To make best use of this topic, you need to download the Maths Helper Plus software. Click here for instructions.

### Theory:

Consider this right angled triangle:

Side ‘p’ is opposite to angle ‘P’, and side ‘q’ is adjacent to angle ‘P’.  (‘Adjacent’ means ‘beside’).

In right angled triangles, the terms 'opposite' and ‘adjacent’ is never used to refer to the longest side opposite to the right angle. This is always called the ‘hypotenuse’. Only the shorter sides, the ‘legs’ of the right triangle, can be 'opposite' or ‘adjacent’ sides.

For angle ‘Q’, side ‘q’ is the opposite side, and side ‘p’ is the adjacent side. For an angle less than 90º in a right angled triangle, the following ratio:

 is called the ‘tangent ratio’ of the angle.

For example, the tangent ratio of angle ‘P’ above can be found as follows:

In the triangle below, the two leg lengths are given, so the tangent ratio for angles 'P' and 'Q' can be calculated:

### Method:

Maths Helper Plus can calculate tangent ratios if the leg lengths of a right triangle are given. It will show the calculations and display a labelled diagram of the triangle.

#### Step 2  Display the parameters box

Press the F5 key to display the parameters box:

You enter the given information into these edit boxes as follows:

edit box 'A' = the vertical leg of the triangle

edit box 'B' = the horizontal leg of the triangle

edit box 'C' = the scale factor for the triangle. ( Leave set to 1)

Edit box 'X' determines which side is adjacent and which is opposite. If 'X' = 1, then the vertical leg 'A' is the opposite side, and 'B' is the adjacent side. If 'X' = 2, then 'A' is adjacent and 'B' is opposite.

Set  A, B to the required leg lengths, then click the 'Update' button to refresh the diagram and calculations.

Enter the values of 'A' and 'B' as given in the examples above. Then try some other numbers of your own.