Sine and Cosine Law (10A)

Establish the sine, cosine and area rules for any triangle and solve related problems (VCMMG367)

LO: To utilise the sine and cosine laws to solve problems involving non-right angled triangles.

Know:

  • the trigonometric ratios and how to use them in context.
  • how to utilise a calculator to fine unknown values.

Understand:

  • That the sine and cosine laws can assist us to find the features of non-right angled triangles.

Do:

  • I can utilise the sine and cosine laws to solve problems involving non-right angled triangles.

Properties of Right-Angled Triangles

“Opposite” is the opposite to the angle.
“Adjacent” is next to to the angle.
“Hypotenuse” is the long side of the right-angled triangle.

Sine Law

Remember the Sine Law can only be utilised for non-right angled triangles.

The Sine Law involves finding matching pairs.

The side involved with the matching sets is always the opposite of the angle.

Notice in the picture to the left, angle “A” is the opposite of side “a” and angle “B” is opposite to the side “b”.

Cosine Law

We utilise the Cosine Law when we don’t have enough matching set information to use the Sine Law.

There are 3 formulas (see left) that you can use to figure out the relevant information.

Sine Law Videos

Cosine Law Videos

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