## 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°=$\frac{\pi }{180}$

#### Examples of converting between degrees and radians

• $\frac{\pi }{180}$$\frac{\pi }{3}$
• $\frac{\pi }{180}$$\frac{5\pi }{6}$
• $\frac{\pi }{5}$$\frac{180°}{5}$
• $\frac{3\pi }{4}$$\frac{3}{4}$

There are five different types of triangle: Equilateral Triangle (three equal sides) Isosceles Triangle (two equal sides) Right Triangle (with a right angle) Acute triangle (all angles less than 90°) Obtuse Triangle (one angle more than 90°)

The three interior angles of a triangle always sum to 180°. Area = $\frac{1}{2}$bh

#### Examples

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

Area = $\frac{1}{2}$ × (10m) × (5m) = 25m2

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

27m2 = $\frac{1}{2}$ × (9m) × h
54m2 = (9m) × h
6m = h

Therefore, height is 6 metres.

## Activity

You can download a version of this Triangles activity in Word format: