Monday, January 26, 2009

Elearn Geometry Problem 184: Triangle, Angles

Proposed Geometry Problem and Solutions.


Triangle and angles

See complete Problem 184 at:
www.gogeometry.com/problem/p184_triangle_angles_problem.htm

The following solution was received from Ibrahim Elsager.

Problem 184 solution. Triangle and angles


Post your solutions or ideas in the comments.

Posted by Antonio Gutierrez at 7:39 AM
Labels: , , ,

1 comment:

  1. MarcoFebruary 17, 2023 at 11:56 PM

    <ABD=<ADB=(180-64)/2=58
    <ACB=180-48-58-30=44
    <ADC=180-16-x=164-x

    Consider Triangle ABC
    sin44/AB=sin(58+30)/AC
    AB/AC=sin44/sin88=1/2cos44--------(1)

    Consider Triangle ADC
    sinx/AD=sin(164-x)/AC
    AD/AC=sinx/sin(164-x)-------(2)

    Since AB=AD, by equating (1) & (2)
    1/2cos44=sinx/sin(164-x)
    sin(164-x)=2sinxcos44
    sin164cosx-cos164sinx=2sinxcos44
    sin164cosx=2sinxcos44+cos164sinx
    sin164cosx=sinx(2cos44+cos164)
    tanx=sin164/(2cos44+cos164)
    x=30

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