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Skills for Learning

Maths & Stats - Trigonometry

Learning Outcomes

If you work through this section you should be able to:

  • Identify different types of angles.
  • Convert between degrees and radians.
  • Identify different types of triangles.
  • Calculate the area.

Angles are used to measure the amount by which a line has been turned. A full circle is 360 degrees.

There are five different types of angle: 
  • Acute angle: θ<90°
  • Right angle: θ=90°
  • Obtuse angle: 180°>θ>90°
  • Straight angle: θ=180°
  • Reflex angle: θ>180°
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Degrees and radians are the two commonly used units in measuring angles.

A circumference of a circle measures 2πr, so the number of radians in a full circle is 2π. Therefore:

  • 360° = 2π
  • π = 180°
  • 1°=π180

Examples of converting between degrees and radians

  • 60° = 60×π180 = π3
  • 150° = 150×π180 = 5π6
  • π5 = 180°5 = 36°
  • 3π4 = 34×180° = 135°

There are five different types of triangle:

Equilateral Triangle Equilateral Triangle
(three equal sides)
Isosceles Triangle Isosceles Triangle
(two equal sides)
Right Triangle Right Triangle
(with a right angle)
Acute triangle Acute triangle
(all angles less than 90°)
Obtuse Triangle Obtuse Triangle
(one angle more than 90°)

The three interior angles of a triangle always sum to 180°.

Diagram shwoing how ot calculate the area of a traingle.

Area = 12bh

Examples

  • Find the area of a triangle with a base of 10 metres and a height of 5 metres.

    Area = 12 × (10m) × (5m) = 25m2

  • The area of a triangle shaped mat is 27 square metres and the base is 9 metres. Find the height.

    27m2 = 12 × (9m) × h
    54m2 = (9m) × h
    6m = h

    Therefore, height is 6 metres.

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