Geometry Problem?

Find x.

Attachment image

2 Answers

Relevance
  • Pope
    Lv 7
    1 month ago

    I am not sure how clear this image will appear, but it should be easier to form a picture if you have it plotted to scale. All of those labeled angle measures should be easy enough to derive by walking through the triangles.

    EB/ED = ABsin(5°) / [ADsin(25°)]

    EB/ED = sin(80°)sin(5°) / [sin(70°)sin(25°)]

    ED/EC = sin(45°)/sin(30°) = √(2)

    EB/EC = (ED/EC)(EB/ED)

    EB/EC = √(2)sin(80°)sin(5°) / [sin(70°)sin(25°)]

    Let this ratio EB/EC be called r.

    r ≈ 0.3057

    EB/EC = sin(x) / sin(105° - x)

    sin(x) / sin(105° - x) = r

    sin(x) = rsin(105° - x)

    sin(x) = rsin(105°)cos(x) - rsin(x)cos(105°)

    sin(x)[1 + rcos(105°)] = rsin(105°)cos(x)

    tan(x) = rsin(105°) / [1 + rcos(105°)]

    x ≈ 17.78°

    Attachment image
  • 1 month ago

    = 80 + 30 = 110°

    =180 - 110 - 25 =45°

    25 + 5 = 30°

    180 - 80 - 30 = 70°

    180 - 70 - 5 = 105°

    180 - 105 = 75°

    180 - 75 = 105°

    180 - 105 - 30 = 45°

    x + 45 + 30 = 180

    x +75 = 180

    x = 180 - 75

    x = 105 Answer//

Still have questions? Get your answers by asking now.