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Maths-

General

Easy

Question

$l n invisible function application a capital delta A B C blank i f blank a to the power of 2 end exponent s i n invisible function application left parenthesis B minus C right parenthesis plus b to the power of 2 end exponent s i n invisible function application left parenthesis C minus A right parenthesis plus c to the power of 2 end exponent s i n invisible function application left parenthesis A minus B right parenthesis equals 0 blank comma blank t h e n text triangle is end text$

right-angled
obtuse angled
isosceles
None of these

The correct answer is: isosceles

Consider
$table row cell a to the power of 2 end exponent s i n invisible function application left parenthesis B minus C right parenthesis equals 2 a R s i n invisible function application left parenthesis B plus C right parenthesis s i n invisible function application left parenthesis B minus C right parenthesis end cell row cell equals 2 a R open parentheses sin to the power of 2 end exponent invisible function application B minus sin to the power of 2 end exponent invisible function application C close parentheses equals fraction numerator a over denominator 2 R end fraction open parentheses b to the power of 2 end exponent minus c to the power of 2 end exponent close parentheses end cell end table$
Similarly, $b to the power of 2 end exponent s i n invisible function application left parenthesis C minus A right parenthesis equals fraction numerator b over denominator 2 R end fraction open parentheses c to the power of 2 end exponent minus a to the power of 2 end exponent close parentheses$
and
$c to the power of 2 end exponent s i n invisible function application left parenthesis A minus B right parenthesis equals fraction numerator c over denominator 2 R end fraction open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses$
$text Therefore, end text$
$table row cell a to the power of 2 end exponent s i n invisible function application left parenthesis B minus C right parenthesis plus b to the power of 2 end exponent s i n invisible function application left parenthesis C minus A right parenthesis plus c to the power of 2 end exponent s i n invisible function application left parenthesis A minus B right parenthesis equals 0 end cell row cell rightwards double arrow a open parentheses b to the power of 2 end exponent minus c to the power of 2 end exponent close parentheses plus b open parentheses c to the power of 2 end exponent minus a to the power of 2 end exponent close parentheses plus c open parentheses a to the power of 2 end exponent minus b to the power of 2 end exponent close parentheses equals 0 end cell row cell rightwards double arrow a left parenthesis b minus c right parenthesis left parenthesis b plus c right parenthesis plus b c to the power of 2 end exponent minus b to the power of 2 end exponent c minus a to the power of 2 end exponent b plus a to the power of 2 end exponent c equals 0 end cell row cell rightwards double arrow a left parenthesis b minus c right parenthesis left parenthesis b plus c right parenthesis minus b c left parenthesis b minus c right parenthesis minus a to the power of 2 end exponent left parenthesis b minus c right parenthesis equals 0 end cell row cell rightwards double arrow left parenthesis b minus c right parenthesis open parentheses a b plus a c minus b c minus a to the power of 2 end exponent close parentheses equals 0 end cell row cell rightwards double arrow left parenthesis b minus c right parenthesis left parenthesis c minus a right parenthesis left parenthesis a minus b right parenthesis equals 0 end cell row cell rightwards double arrow text end text text E end text text i end text text t end text text h end text text e end text text r end text text end text a equals b text end text text o end text text r end text text end text b equals c text end text text o end text text r end text text end text c equals a end cell end table$

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