Introduction to the
||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
here for instructions.
Consider this right angled
Side ‘p’ is opposite
to angle ‘P’, and side ‘q’ is adjacent to angle ‘P’.
(‘Adjacent’ means ‘beside’).
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:
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
Step 1 Download
the free support file...
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.
name: 'Tangent ratio 1.mhp' File size: 10kb
Click here to download the file.
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
Step 2 Display
the parameters box
Press the F5 key to display the
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
box 'C' = the scale factor for the triangle. ( Leave set to 1)
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.
A, B to the required leg lengths, then click the 'Update' button to refresh the
diagram and calculations.
the values of 'A' and 'B' as given in the examples above. Then try some other
numbers of your own.
Still don't understand or
have further questions about this topic ?
Then ask us! Click