when 2 sides   ex 7cm ,9cm how to find 3rd sins

Asked by madhavi.lathag | 26th Nov, 2014, 09:25: PM

Expert Answer:

G i v e n space t w o space s i d e s space o f space a space t r i a n g l e comma space i t space i s space n o t space p o s s i b l e space t o space f i n d space t h e space t h i r d space s i d e space o f space t h e space t r i a n g l e. T h e space a n g l e space o p p o s i t e space t o space t h e space u n k n o w n space s i d e space i s space n e e d e d space t o space f i n d space t h e space t h r i d space s i d e space o f space t h e space t r i a n g l e. C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.
S u p p o s e space a equals 7 space c m space a n d space b equals 9 space c m O u r space a i m space i s space t o space f i n d space t h e space t h i r d space s i d e space apostrophe c apostrophe. F o r space t h a t space w e space n e e d space a n g l e space C. C o n s i d e r space t h e space f o l l o w i n g space cos i n e space f o r m u l a : c squared equals a squared plus b squared minus 2 cross times a cross times b cross times cos open parentheses C close parentheses... left parenthesis 1 right parenthesis I f space t h e space a r e a space o f space t h e space t r i a n g l e space i s space k n o w n : A r e a equals 1 half cross times a cross times b cross times sin open parentheses C close parentheses rightwards double arrow sin open parentheses C close parentheses equals fraction numerator 2 cross times A r e a over denominator a cross times b end fraction rightwards double arrow C equals sin to the power of minus 1 end exponent open parentheses fraction numerator 2 cross times A r e a over denominator a cross times b end fraction close parentheses.... left parenthesis 2 right parenthesis S u b s t i t u t i n g space t h e space v a l u e space o f space C space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma c squared equals a squared plus b squared minus 2 cross times a cross times b cross times cos open parentheses sin to the power of minus 1 end exponent open parentheses fraction numerator 2 cross times A r e a over denominator a cross times b end fraction close parentheses close parentheses rightwards double arrow c equals square root of a squared plus b squared minus 2 cross times a cross times b cross times cos open parentheses sin to the power of minus 1 end exponent open parentheses fraction numerator 2 cross times A r e a over denominator a cross times b end fraction close parentheses close parentheses end root W e space a p p r e c i a t e space y o u r space c u r i o s i t y space i n space k n o w i n g space t h i n g s. B u t space t h i s space i s space n o t space o f space y o u r space c u r r i c u l u m space a n d space y o u space m a y space f i n d space i t space d i f f i c u l t space t o space u n d e r s tan d. P l e a s e space d o space p o s t space q u e r i e s space i f space y o u space a r e space h a v i n g space a n y space d o u b t.

Answered by Vimala Ramamurthy | 27th Nov, 2014, 09:21: AM

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