Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the degree measure of the angle subtended at the centre of a circle of radius 100

cm by an arc of length 22 cm (Use straight pi space equals space 22 over 7).

Answer

r = 100 cm,             l = 22 cm
Now,          l over r space equals space straight theta space left parenthesis in space radians right parenthesis space space space space space space space space space space space space rightwards double arrow space space space space space space space space space space space space space straight theta space equals space open parentheses 22 over 100 close parentheses to the power of straight c space equals space open parentheses 11 over 50 close parentheses to the power of straight c
rightwards double arrow             straight theta space equals space open parentheses 11 over 50 space cross times space 180 over straight pi close parentheses to the power of ring operator space equals space open parentheses 11 over 50 cross times 180 cross times 7 over 22 close parentheses to the power of ring operator space equals space open parentheses 63 over 5 close parentheses to the power of ring operator space equals space 12 open parentheses 3 over 5 space cross times space 60 close parentheses to the power of comma space equals space 12 degree 36 apostrophe

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