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CBSE Class 10 Answered

In triangle abc angle a is equal to 60degrees prove that bc^2=ab^2+ bc ^2-ab.ac
Asked by vibhu.wwe | 14 Feb, 2018, 05:15: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon
In space increment ABC comma space angle straight A equals 60 degree
To space prove colon
BC squared equals AB squared plus BC squared minus AB cross times AC
Proof colon space
Draw space CD perpendicular AB
In space increment CDB comma
CD squared plus BD squared equals BC squared
CD squared equals BC squared minus BD squared......... left parenthesis straight i right parenthesis
Also comma space in space increment CDA
CD squared plus DA squared equals CA squared
CD squared equals CA squared minus DA squared........ left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis
BC squared minus BD squared equals CA squared minus DA squared
BC squared equals CA squared minus DA squared plus BD squared
BC squared equals CA squared minus DA squared plus open parentheses AB minus AD close parentheses squared
BC squared equals CA squared minus up diagonal strike DA squared end strike plus AB squared minus 2 AB cross times AD plus up diagonal strike AD squared end strike
BC squared equals CA squared plus AB squared minus 2 AB cross times AD......... left parenthesis iii right parenthesis
In space increment CDA comma
cos 60 degree equals AD over AC
1 half equals AD over AC
AD equals AC over 2............... left parenthesis iv right parenthesis
From space left parenthesis iii right parenthesis space and space left parenthesis iv right parenthesis
BC squared equals CA squared plus AB squared minus 2 AB cross times AC over 2 space space space space space space space space space space space space end style
Answered by Sneha shidid | 14 Feb, 2018, 05:43: PM
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