tag:blogger.com,1999:blog-6933544261975483399.post3890487254537539108..comments2024-03-26T19:10:02.918-07:00Comments on Go Geometry (Problem Solutions): Elearn Geometry Problem 184: Triangle, AnglesAntonio Gutierrezhttp://www.blogger.com/profile/04521650748152459860noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6933544261975483399.post-87288855446560306212023-02-17T23:56:27.810-08:002023-02-17T23:56:27.810-08:00<ABD=<ADB=(180-64)/2=58
<ACB=180-48-58-30...<ABD=<ADB=(180-64)/2=58<br /><ACB=180-48-58-30=44<br /><ADC=180-16-x=164-x<br /><br />Consider Triangle ABC<br />sin44/AB=sin(58+30)/AC<br />AB/AC=sin44/sin88=1/2cos44--------(1)<br /><br />Consider Triangle ADC<br />sinx/AD=sin(164-x)/AC<br />AD/AC=sinx/sin(164-x)-------(2)<br /><br />Since AB=AD, by equating (1) & (2)<br />1/2cos44=sinx/sin(164-x)<br />sin(164-x)=2sinxcos44<br />sin164cosx-cos164sinx=2sinxcos44<br />sin164cosx=2sinxcos44+cos164sinx<br />sin164cosx=sinx(2cos44+cos164)<br />tanx=sin164/(2cos44+cos164)<br />x=30Marcohttps://www.blogger.com/profile/04632526355171968456noreply@blogger.com