Transcript Area of Triangle File

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
• Often 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.
▫ Angle A is opposite side a (at point A)
▫ Angle B is opposite side b (at point B)
▫ 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.
opp
sin  
hyp
h
sin C 
b
 h  b sin 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 cm2. Show that the included
angle may have two possible sizes.