Principle of Mathematical Induction

Principle of Mathematical Induction

Question

In triangle ABC, if a = 18, b = 24, c = 30, find sin C



Answer

Area of triangle ABC = space space 1 half ab space sinC space equals space square root of straight s space left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis end root
rightwards double arrow                  sin space straight C space equals space fraction numerator 2 square root of straight s left parenthesis straight s minus straight a right parenthesis space left parenthesis straight s minus straight b right parenthesis space left parenthesis straight s minus straight c right parenthesis end root over denominator ab end fraction space equals space fraction numerator 2 cross times square root of 36 left parenthesis 36 minus 18 right parenthesis space left parenthesis 36 minus 24 right parenthesis space left parenthesis 36 minus 30 right parenthesis end root over denominator 18 cross times 24 end fraction
                                equals space fraction numerator 2 cross times 216 over denominator 18 cross times 24 end fraction space equals space 1

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