Area of Triangles Non Right-Angled Triangle Trigonometry By the end of this lesson you will be able to explain/calculate the following: 1.Area of Right-Angled Triangles 2.Area of Non Right-Angled Triangles

non–right-angledOften the triangle that is identified in a given problem is non–right-angled. Thus, Pythagoras’ theorem or the trigonometric ratios are not as easily applied. The two rules that can be used to solve such problems are: 1.the sine rule, and 2.the cosine rule.

For the sine and cosine rules the following labelling convention should be used. Aa ▫Angle A is opposite side a (at point A) Bb ▫Angle B is opposite side b (at point B) Cc ▫Angle C is opposite side c (at point C) ▫To avoid cluttered diagrams, only the points (A, B and C) are usually shown and are used to represent the angles A, B & C.

We can use the area formula to find the included angle between two sides We need to use the inverse sine ratio ▫denoted as sin -1 A triangle has sides of length 10 cm and 11 cm and an area of 50 cm 2. Show that the included angle may have two possible sizes.