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Mathematics for science and technology
Mathematics for science and technology

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1 Right angled triangles

It is a triangle in which one of the angles is 90°, which is commonly referred to as a right angle. The sum of the angles in any triangle is 180°. So if the other two angles are α (alpha) and β (beta) as shown in Figure 1 then:

multiline equation row 1 sum with, 3 , summands alpha plus beta plus 90 degree equals 180 degree row 2 alpha plus beta equals 90 degree
A right angle triangle.
Figure 1 A right angle triangle

Look at the angle β in Figure 1. The side of the triangle opposite to this is labelled b and is called the ‘opposite’. The side next to β is labelled a and is referred to as the ‘adjacent’. The side labelled c is the called the ‘hypotenuse’. The hypotenuse is always the side opposite the right angle.

Pythagoras’ Theorem states that the square of the length of the hypotenuse of a right angle triangle is equal to the sum of the squares of the lengths of the other two sides. Looking at the triangle in Figure 1 this gives:

equation left hand side c squared equals right hand side a squared plus b squared

This formula, together with some knowledge of trigonometry enables us to calculate the angles and sides of the triangle in Figure 1 (given some other information).

Now look at a calculator and make sure that it is set in scientific mode if you are using a calculator on a mobile device or PC. Scientific calculators operate in at least two modes when dealing with angles. Before embarking on any of the examples please ensure that your calculator is in degree mode. This is usually the default option. To check that your calculator is set to degrees try this activity.

Activity 1 Calculator in degrees

Timing: Allow about 5 minutes

Use your calculator to work out the value of the following:

  1. sin 60
  2. cos 60
  3. tan 60

Whether you need to press the function button or enter the number first will depend upon the calculator you are using.


If your calculator is set in degrees your answers will be:

  1. sin 60 = 0.8660 (to 4 significant figures)
  2. cos 60 = 0.5
  3. tan 60 = 1.732 (to 4 significant figures)

If your calculator is set in radians your answers will be:

  1. sin 60 = –0.3048 (to 4 significant figures)
  2. cos 60 = –0.9524 (to 4 significant figures)
  3. tan 60 = 0.3200 (to 4 significant figures)

Make sure before you proceed that you change your calculator to degree mode. If you are unsure how to do this you can try searching the internet.

The three functions that you used in this activity (sin, cos and tan) are the basic trigonometric (or ‘trig’) functions. These functions will be the subject of the remainder of the week.