ABC is a triangle with sides a,b and c. show that : if then A=2B I try to use the cosine law, but no result
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Originally Posted by razemsoft21 ABC is a triangle with sides a,b and c. show that : if then A=2B I try to use the cosine law, but no result In any isosceles straight-angle triangle with hypotenuse and legs we have, by Pythagoras, that , but nevertheless , and thus the claim is false. Tonio
Hello, razemsoft21! We are given: . Law of Cosines: .[1] . . . . . . . . . . . . . . . . . . .[2] Since [1] = [2], we have: . . . Therefore: .
Originally Posted by tonio In any isosceles straight-angle triangle with hypotenuse and legs we have, by Pythagoras, that , but nevertheless , and thus the claim is false. Tonio Our triangle is not isosceles, and it is not aright-angled triangle. and I think we cann't use Pythagoras theorem.
Originally Posted by Soroban Hello, razemsoft21! We are given: . Law of Cosines: .[1] . . . . . . . . . . . . . . . . . . .[2] Since [1] = [2], we have: . . . Therefore: . Very nice. In my example I confused between , since clearly ...*sigh* Of course, this would have hardly happend had the OP written ... Tonio
Originally Posted by razemsoft21 ABC is a triangle with sides a,b and c. show that : if then A=2B I tried to use the cosine law, but no result. Another way.... We have an alternative expression for this fraction using the Sine Law Using the identity
Originally Posted by Archie Meade Another way.... We have an alternative expression for this fraction using the Sine Law Using the identity GOOD job .... under stood .... THANKS