Saved Bookmarks
| 1. |
a,b,c are the lengths of three sides of triangle ABC. If a, b c are releated by the releation `a^(2)+b^(2)+c^(2)`=`ab+bc+ca`, then the value ofA. `(3)/(4)`B. `(3)/(2)`C. `(3sqrt3)/(2)`D. `(9)/(4)` |
|
Answer» Correct Answer - d ` a^(2)+b^(2)+c^(2)=ab+bc+ca` or `a^(2)+b^(2)+c^(2)-ab-bc-ca=0` or `2a^(2)+2b^(2)+2c^(2)-2ab-2bc-2ca=0` or `a^(2)+b^(2)-2ab+b^(2)+c^(2)-2bc+c^(2)+a^(2)-2ca=0` ` (a-b)^(2)+(b-c)^(2)+(c-a)^(2)=0` `therefore `a=b=c` DeltaABC=` equllateral`Delta` `therefore angleA=angleB=angleC=60^(@)` So,`sin^(2)A+sin^(2)B+sin^(2)C` `=sin^(2)60^(@)+sin^(2)60^(@)+sin^(2)60^(@)` `=3((sqrt(3))/(2))^(2)` `(9)/(4)` |
|