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Math Help - Using trig to find a sidelength?

  1. #1
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    Using trig to find a sidelength?

    In a triangle ABC, X is a point on AC so that (AX/XC) = 3 and angle AXB = 70 degrees. Find the length of AC if angle ABC = 110 degrees and BC = 6 cm

    I don't know if this fits under trigonometry or geometry, but it is a triangle. My teacher has hinted that similar triangles may be involved. Thanks to anyone who helps.
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  2. #2
    Like a stone-audioslave ADARSH's Avatar
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    ..

    <XCB=<BCA
    <BXC=<ABC
    Hence triangles ABC & XBC are similar
    so
    AB/XB= BC/XC = AC/BC

    BC^2=AC*XC...(1)
    now
    AC/XC=4/1
    =>AC/4=XC
    so
    put XC in (1)
    u get (AC^2)/4=36
    hence AC=12
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