in the given fig length of bc=a, ac=b and ab=c
then prove that ar of abc is equal to 1/2absinc

Asked by Sanmit Ratnaparkhi | 12th Aug, 2014, 06:42: PM

Expert Answer:

W e space k n o w space t h a t space A r e a space o f space t r i a n g l e space equals space 1 half cross times b a s e cross times H e i g h t H e r e space h e i g h t space i s space l e n g t h space o f space a l t i t u d e space f r o m space o p p o s i t e space v e r t e x space t o t h e space b a s e S o space L e t s space c o n s i d e r space B C space a s space b a s e space a n d space A D space i s space A l t i t u d e space f r o m space A space t o space B C rightwards double arrow A r e a space o f space T r i a n g l e equals 1 half cross times B C cross times A D b u t space g i v e n space B C equals a space a n d space w e space k n o w space t h a t space f r o m space t r i a n g l e space A D C A D C space i s space r i g h t space a n g l e d space t r i a g n l e space a s space A D space i s space a l t i t u d e. space S o space S i n space C space equals space fraction numerator A D over denominator A C end fraction rightwards double arrow A D equals A C space S i n space C S u b s t i t u t e space t h e space v a l u e s space o f space A D equals A C space S i n space C comma space B C equals a space a n d space A C equals b W e space g e t space A r e a space o f space T r i a n g l e equals 1 half open parentheses a b close parentheses S i n space C

Answered by Dharma Teja | 13th Aug, 2014, 07:46: AM

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