What is the sine rule?

• The sine rule allows us to find missing side lengths or angles in?non-right-angled triangles
• It states that for any triangle with angles?A, B?and?C

• • Where
    • a?is the side?opposite?angle?A
    • b?is the side?opposite?angle?B
    • c?is the side?opposite?angle?C
• This formula?is in the formula booklet, you do not need to remember it
• Sin 90° = 1 so if one of the angles is 90° this becomes SOH from?SOHCAHTOA

How can we use the sine rule to find missing side lengths or angles?

• The sine rule can be used when you have any opposite pairs of sides and angles
• Always?start by labelling your triangle?with the angles and sides
  • Remember the sides with the lower-case letters are?opposite?the angles with the equivalent upper-case letters
• Use the formula in the formula booklet to find the?length of a side
• To find a missing angle you can rearrange the formula and use the form

• • This is?not in the formula booklet?but can easily be found?by rearranging?the one given

• Substitute the values you have into the formula and solve

What is the cosine rule?

• The cosine rule allows us to find missing side lengths or angles in?non-right-angled triangles
• It states that for any triangle
• Where
  • c?is the side?opposite?angle?C
  • a?and?b?are the other two sides

• Both of these formulae?are in the formula booklet, you do not need to remember them
  • The first version is used to find a missing side
  • The second version is a rearrangement of this and can be used to find a missing angle
• Cos 90° = 0 so if C = 90° this becomes?Pythagoras’ Theorem

How can we use the cosine rule to find missing side lengths or angles?

• The cosine rule can be used when you have two sides and the angle between them or all three sides
• Always?start by labelling your triangle?with the angles and sides
  • Remember the sides with the lower-case letters are?opposite?the angles with the equivalent upper-case letters
• • C?is the angle?between?sides?a?and?b
• Substitute the values you have into the formula and solve

How do I find the area of a non-right triangle?

• The area of?any triangle can be found using the formula

• • Where?C?is the angle between sides?a?and?b

• • This formula?is in the formula booklet, you do not need to remember it
• Be careful to label your triangle correctly so that?C?is always the angle?between?the two sides
• Sin 90° = 1 so if C = 90° this becomes Area = ? × base × height