To calculate: The central angle in radians.
The angle’s are
The length of the chord AB is 4 cm.
The length of the arc AB is 5cm.
We seek a solution of , starting from an initial estimate .
For , compute the next approximation by
and so on.
Formula: where s is arc length, r is the radius of the circle and is the central angle.
Law of cosine where a , b , c are sides of triangle .
Length of the chord is 4cm.
Length of the arc is 5 cm.
Now , using law of cosine we have ,
Putting (i) in (ii) we get,
Hence, we get
Now, let initial approximation be
The second approximation is .
The third approximation is .
Hence , the central angle in radians are :-
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