calcul de l′ angle x
△ABD ((sin y)/(AD))=((sin44 )/(BD)) (1)
△ADC ((sin x)/(AD))=((sin48 )/(DC)) (2)
(1) BD sin y=ADsin 44
(2) DCsinx =ADsin 48
(((1))/((2)))⇔ ((BDsin y)/(DCsin x))=((sin 44)/(sin 48)) (3)
△BDC ((sin 14)/(BD))=((sin 28)/(DC))
((BD)/(DC))=((sin 14)/(sin 28))
(3)⇔((sin 14×)/(sin 28×))((sin y)/(sin x))=((sin 44)/(sin 48))
Relation entre x et y
△ABC (∡A +∡B+ ∡C)=180
48+44+y+28+14+x=180
x+y=46 ⇒ y=46−x
((sin x)/(sin y))=((sin 48×sin 28)/(sin 44×sin 14))
((sinx)/(sin(46−x)))=((2sin 48×cos 14)/(sin 44))
=((sin x)/(sin 46cos x−cos 46sin x))
=((sin x)/(cos x(sin 46−tan x×cos 46)))
=((tan x)/(sin 46−cos 46×tan x))
sin 44×tan x=2sin 48×cos 14(sin 46−cos 46tan x)
(sin 44+2sin 48cos 14×cos 46)tan x=
2sin 48cos 14×sin 46
tan x=((2sin 48×cos 14×sin 46)/(sin 44+2sin 48×cos 14×cos 46))
sin 44= sin 48= sin 46
cos 14= cos 46=
tan x=0,61150462
soit: X=31,446^°
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