!set title=Producto escalar y coseno
!if $wims_read_parm!=$empty
 !goto $wims_read_parm
!endif
oef2wims_version=3.22
language=fr
author=René Chaffard
email=chafrene@club-internet.fr
computeanswer=no
precision=1000

ansorder=r
varcnt=14
prevarcnt=13
postvarcnt=0
replycnt=1
choicecnt=0
conditioncnt=0
feedbackcnt=1
format=html

val1=$imagedir
val2=$confparm1
val3=$confparm2
val4=$confparm3
val5=$confparm4

!if $testcondition=yes
 !goto test
!endif
!if $status=waiting
 !exit
!endif

tmp0=!randitem a,b,c

val6=$(tmp0)
tmp0=!shuffle A,B,C

val7=$(tmp0)
val8=$(val7[1])
val9=$(val7[2])
val10=$(val7[3])
tmp0=!randint 2, 8

val11=$[rint($(tmp0))]
tmp0=!randint 2, 8

val12=$[rint($(tmp0))]
val13=$[rint(abs($val11-$val12)+1)]
val14=$[rint($val11+$val12-1)]
tmp0=!randint $val13, $val14

val15=$[rint($(tmp0))]
tmp=!translate ";': to $     $ in ($val11^2+$val12^2-$val15^2)/2

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val16=$(tmp0)
tmp0=!shuffle \($val8$val9 = $val11 ) , \($val9$val10 = $val15) ,  \($val10$val8 = $val12)

val17=$(tmp0)
tmp=!translate ";': to $     $ in ($val16)/($val11*$val12)

tmp=!lower $tmp
tmp0=!exec maxima fullratsimp($tmp);
val18=$(tmp0)
replyname1=cosinus :
replygood1=$val18
question=__EXECUTED_1692754_EXERCISE__
hint=__EXECUTED_1692754_EXERCISE__
solution=__EXECUTED_1692754_EXERCISE__

!goto stat

!exit

:question
$()	Se considera un triángulo 
!insmath ABC
$() tal que :	<p style="text-align:center"> $(val17[1]),  $(val17[2]), $(val17[3]). </p>	Calcular	<p style="text-align:center">
!insmath  cos(\widehat{\overrightarrow{$val8$val9},\overrightarrow{$val8$val10}})
$() 	=  
!read oef/embed.phtml reply1,10 
$(). </p>		
$()
!exit

:hint
$()Dos estrategias equivalentes :<br/>	<ul><li>comenzar por calcular un producto escalar convenientemente elegido y considerar la fórmula :	<center>
!insmath  \overrightarrow{$val8$val9} \cdot \overrightarrow{$val8$val10}  = $val8$val9.$val8$val10.\cos(\hat{A})
$()</center>	</li><li>utilizar el teorema de Al-Kashi</li></ul>
$()
!exit

:help
$()
$()
!exit

:solution
$()	<br>	
!insmath  \overrightarrow{$val8$val9} \cdot \overrightarrow{$val8$val10} = $val16 
$()	donc :
!insmath $val16 = $val12\times $val11\times  cos(\widehat{\overrightarrow{$val8$val9},\overrightarrow{$val8$val10}})
$()
$()
!exit

:feedback
!ifval $m_reply1<-1 or $m_reply1>1
 <p><b>Atención !</b> el valor del coseno de un ángulo debe pertenecer al intervalo [-1,1]
$()
!endif

!exit

:test

!exit

:stat
vsavelist=8,9,10,11,12,16,17
embedcnt=1
