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Question Number 189290 by normans last updated on 14/Mar/23

Answered by a.lgnaoui last updated on 14/Mar/23

△ABC [∡OAC=x ∡BAO=y] x+y=180−126=54 △AOB : ((sin 25)/(OA))=((sin y)/(OB)) (1) △AOC : ((sin 17)/(OA))=((sin x)/(OC)) (2) (((1))/((2)))⇒((sin 25)/(sin 17))=((sin y)/(sin x))×((OC)/(OB)) (3) △BOC : ((sin 38)/(OC))=((sin 46)/(OB)) ⇒ ((OC)/(OB))=((sin 38)/(sin 46)) (4) (3)⇔((sin 25)/(sin 17))=((sin y)/(sin x))×((sin 46)/(sin 38)) ⇒((sin (54−x))/(sin x))=((sin 25)/(sin 17))×((sin 38)/(sin 46)) sin (54−x)=(((sin 25sin 38)/(sin 17sin 46)))sin sin x sin 54cos x=(cos54+((sin 25sin 38)/(sin 17sin 46)))sin x tan x=(( sin 54sin 17sin 46)/(cos 54sin 17sin 46+sin 25sin 38)) tan x=0,4433137846933 (x=23,90837..) x≅24

△ABC[∡OAC=x∡BAO=y]x+y=180−126=54△AOB:sin25OA=sinyOB(1)△AOC:sin17OA=sinxOC(2)(1)(2)⇒sin25sin17=sinysinx×OCOB(3)△BOC:sin38OC=sin46OB⇒OCOB=sin38sin46(4)(3)⇔sin25sin17=sinysinx×sin46sin38⇒sin(54−x)sinx=sin25sin17×sin38sin46sin(54−x)=(sin25sin38sin17sin46)sinsinxsin54cosx=(cos54+sin25sin38sin17sin46)sinxtanx=sin54sin17sin46cos54sin17sin46+sin25sin38tanx=0,4433137846933(x=23,90837..)x≅24

Commented by a.lgnaoui last updated on 14/Mar/23

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