Topic Content:
- Derivation of Cosine Rule
The cosine formula is primarily used to solve triangles with the following dimensions:
(i) Two sides, given, with the angle between them given.
(ii) Three sides of the triangle are given.
Derivation of the Cosine Formula:
Two cases of the derivation shall be considered as follows:
(i) Acute-angled triangle
(ii) Obtuse-angled triangle
Let BD = x
From Fig. i
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CD = a – x
From Fig. ii
CD = x – a
In ∆ABD (in both figures):
AD2 = AB2 – BD2 (Pythagoras theorem)
AD2 = c2 – x2 …………. (i)
In ∆ACD (in both figures) :
AD2 = AC2 – CD2 (Pythagoras theorem)
from Fig. i
AD2
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