# Simple Trigonometry of Right-Angled Triangles

This applet investigates the basic trigonometry of right-angled triangles. Users get the chance to choose which of the three ratios (sin, cos, tan) to use in each case.

###### Author and programmer: Ron Barrow

UK Years 9-11, KS3, KS4, Foundation and Higher GCSE Mathematics, Grades C - A* - Data Handling, Shape, Space and Measure

US - Grade9 - Geometry

Instructions below See also: The Pythagoras Rule

Trigonometric ratios:

## How to Use this Applet

On the screen you'll see a right-angled triangle. You can change this triangle by clicking and dragging the vertices (corner points) with the mouse, but it will always have a right-angle in it. You can investigate the use of Trigonometry for finding sides and angles in right-angled triangles, by using the three ratios **sin** (sine), **cos** (cosine) and **tan** (tangent). The ratios involve:

the side OPPOSITE the angle (**O**)

the side ADJACENT (next) to the angle (**A**)

the HYPOTENUSE opposite the right angle (**H**).

You can choose the value you want to calculate by checking one of the three boxes at the bottom left. Two other values are then shown. You must decide which of sin, cos and tan to use in the calculation by selecting one of them at the bottom right of the screen. If you're correct, the working and answer will be seen. If not, you will be asked to try again.

Trigonometry is very important and can solve many problems. It is hard at first but the more you do it the easier it becomes. Use this applet to practise and learn. Enjoy!