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Math Help - Constructions

  1. #1
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    Constructions

    Construct a triangle ABC in which BC = 7 cm, <A = 60o and altitude through A is 3.7 cm. How many such triangles are possible? Please tell me the steps of construction.
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    Quote Originally Posted by ice_syncer View Post
    Construct a triangle ABC in which BC = 7 cm, <A = 60o and altitude through A is 3.7 cm. How many such triangles are possible? Please tell me the steps of construction.
    Description:

    1. Draw line BC
    2. Draw a parallel to BC with the perpendicular distance of h_A
    3. Draw the perpendicular bisector of BC
    4. Draw in B (or in C) the angle of (90 - <(A)) = 30 , that means <(MBC) = 30
    5. The arm of this angle crosses the perpendicular bisector in M.
    6. Draw the circle around M with radius r = MB (or MC)
    7. The intersection points of the circle and the parallel to BC are the points A.
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  3. #3
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    I've attached the construction.
    Attached Thumbnails Attached Thumbnails Constructions-puz2.gif  
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    Quote Originally Posted by earboth View Post
    I've attached the construction.
    Where's the altitude through A ?
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  5. #5
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    Quote Originally Posted by ice_syncer View Post
    Where's the altitude through A ?
    The altitude is the distance between the two parallel lines and because the angle at b (or C respectively) is greater than 90 the altitude lies outside the area of the triangle.
    Attached Thumbnails Attached Thumbnails Constructions-puz2_alti.gif  
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