The Sine Ratio

Key Facts and Exam Tips

A right-angled triangle contains one angle of 90 degrees.

In a right-angled triangle the longest side is opposite the right angle and is called the ‘hypotenuse’.

The other two sides are named in relation to the angle you are working with. The side opposite this angle is called the ‘opposite’. The side next to this angle is called the ‘adjacent’.

You must identify the sides correctly when solving problems using trigonometry. Remember, the longest side is always the hypotenuse.

The sine ratio is constant for a given angle.

Remember the formula ‘sin = opposite / hypotenuse’. This formula can be used to calculate the length of a side or the size of an angle in a right-angled triangle. Practise rearranging the formula to find the length of the opposite side or of the hypotenuse.

Learn how to operate the sine function on your calculator. Make sure you know the order in which to enter values on your machine.

To find an angle, you need to use the inverse-sine function (sin^—1). Again, check that you can do this on your calculator.

Make sure you know how to check whether your calculator is working in degrees, and how to correct it if it isn’t.

When answering exam questions, give your solution to the degree of accuracy asked for in the question; or if this is not specified, to a degree sensible for the situation. It is safest to round at the end of your working, to avoid errors.

Use appropriate units for lengths. These are usually given in the question.