Presentation on theme: "Sine and cosine formula. Non right angled triangles What’s the relationship between a, b and C? Consider area S of right angled triangle, given by base."— Presentation transcript:
Sine and cosine formula
Non right angled triangles What’s the relationship between a, b and C? Consider area S of right angled triangle, given by base and height
The Sine Rule For solving triangles Given Can show that…
Solving triangles with sin rule Note all angles add up to (π radians) Note sin -1 can return θ and 180-θ hence possible ambiguity or = Though 132 invalid because >180
Example 1 Two angles and any one side of a triangle are given In ABC of figure 4, A = 50 , B = 70 and a = 10cm. Solve the triangle. (Answers correct to 3 significant figures 三個 有效數字 if necessary 如必須.) 50 o 70 o a=10cm AB C
Solution From subtraction 減法, C = 60 o By sine formula, AC = 10 x sin 70 o / sin 50 o = 12.3 cm AB = 10 x sin 60 o / sin 50 o = 11.3 cm
Two sides and one non-included angle are given Example 2 In ABC, find B if A = 30 , b = 10cm and a = 4cm.
sinB = 1.25 > 1 which is impossible 不可能的 Hence, no triangle exists for the data given. The situation 情況 can further be illustrated 舉例證明 by accurate 準確 a=4cm b=10cm A=30 o C c B
Example 4 In ABC, find B if A = 30 , b = 10cm and a = 6cm.
Solution By sine formula, sinB = 10x sin30 o /6 sinB = B = 56.4 o, o b=10cm A=30 o a=6cm BB C
Cosine Rule By considering triangle can also show… When an angle and the two sides forming it are given use the cosine rule
Given a triangle ABC, in which a = 28cm, c = 40cm, B = 35 . Find the length AC and correct your answer to 1 decimal place.
Solution By cosine formula, b = 23.4 cm a=28cm 35 o c=40cm C A B b