Introduction to the tangent ratio.





Part 1

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:


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Part 2

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 1 Download the free support file…We have created a Maths Helper Plus document containing the completed example from this topic. You can use this to practice the steps described below, and as a starting point for solving your own problems.

File name: ‘Tangent ratio 1.mhp’ File size: 10kb
Click here to download the file.

If you choose` ‘Open this file from its current location’, then Maths Helper Plus should open the document immediately. If not, try the other option: ‘Save this file to disk’, then run Maths Helper Plus and choose the ‘Open’ command from the ‘File’ menu. Locate the saved file and open it. If you do not yet have Maths Helper Plus installed on your computer, click here for instructions.

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 the 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.

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