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ABCD is a trapezoid with DC parallel to AB, AB=4, AD=4, angle A=60, angle C=45. Find DC and BC

  • geometry -

    Make a sketch, marking all the given data

    join BD
    since AB = AD = 4, the triangle is isosceles, furthermore it is easy to see that it must be equilateral, all angles are 60° and BD = 4

    By alternate angles , angle BDC = 60° leaving angle CBD = 75°
    Using the sine law,
    BC/sin60 = 4/sin45
    BC = 4sin60/sin45 = 4.8989 or appr. 4.9

    find DC in the same way

  • Maths -

    Find the radius of a right circular cyilender whose volume is and height is 20cm.

  • geometry -

    v = pi r^2 h
    3080 = pi * 20 * r^2
    r^2 = 3080/20pi
    r = ...

  • geometry -

    The two triangles above are similar. If XZ = 10 cm, YZ = 15 cm, and AC = 18 cm, what is the length of BC?

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