Non-right-angled Triangles

Patternity_ShapeSections.jpegThe basic trigonometric ratios of sine, cosine and tangent only apply to right-angled triangles.

For non-right-angled triangles, there are three useful rules for finding information, they are the sine rule, the cosine rule and the area formula. The triangle below can be used for the three formulae.

Y11_Non-right-angled_Triangles_01.gif

The Sine Rule

 

When finding the length of a side:

Y11_Non-right-angled_Triangles_02.gif

See proof

See example

When finding the size of an angle:

Y11_Non-right-angled_Triangles_03.gif

The Cosine Rule

 

When finding the length of a side:

a2 = b2 + c2 − 2bc cos A

 

See proof

See example

When finding the size of an angle:

Y11_Non-right-angled_Triangles_04.gif

 

The Area Formula

 

When finding the area of a triangle: 

Area = 0.5 ab sin C

See proof

See example