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Trigonometric Formulae

In any ∆ ABC,
 
Description: P-324-5.tif
 
Area of a triangle
 
Area of ∆ Description: 7113.png bc sin A, where A = BAC
 
 
Area of ∆ Description: 7104.png ac Sin B, where B = ABC
 
 
Area of ∆ Description: 7097.png ab Sin C, where C = ACB

Cosine Rule and Sine Rule

In any ∆, we have six quantities namely the three angles and the three sides. Using the following rules, we can find any of the three quantities if we are provided with the remaining three quantities.
Description: 7090.png
 
Description: 7083.png
 
Description: 7076.png
 
Sine Rule Description: 7069.png
 
Sine and Cosine formulae are particularly more im­portant in cases where we have one side and two angles out of the three angles of the triangle and we have to find out the value of all the sides and angles.
Description: 7062.pngDescription: 7055.png
 
Two important points
  • The side opposite to the largest angle will be the largest.
  • The side opposite to the smallest angle will be the smallest.
Example
In the figure given below, AD = CD = BC. What is the value of ∠CDB?
 
Description: P-325-1.tif
 
Solution
x + y = 180 – 96 = 84° (i)
 
In ∆CDB, 4x + y = 180 (ii)
 
Solving (i) and (ii), x = 32°
So, 2x = 64°
 
Description: P-325-2.tif
 





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