Heron’s Formula (10A)

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

LO: To utilise Heron’s Formula to find the area of non-right angled triangles.

Know:

  • how to multiply 3 sides of a triangle.
  • how to square root a number using digital technologies.

Understand:

  • That Heron’s formula can be utilised to find the area of non-right angled triangles.

Do:

  • I can utilise Heron’s Formula to find the area of 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.

Heron’s Formula

Finding the area of a right-angled triangle is pretty simple. You just need to multiply the base of the triangle by the height and divide the answer by two.

However, with a non-right angled triangle, this is a little bit trickier.

The first step is to find out the value of “S“.

S is basically the perimeter of the triangle divided by two.

Once you know the “S” value, you just have to just apply Heron’s Formula which is the square root of S multiplied by S minus side “A”, S minus side “B” and S minus side “C”.

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

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