Math

I'm doing Similarities in class and have no idea how this question works. Any explanations as to how to do this question would be great. Here it is:

Here is a way to find (roughly) the width of a river without crossing it.
Place a stake B on one bank opposite a landmark A on the other bank. Walk a distance of 5m along the bank at right abgles to AB and place another stake C. Walk another 1m in the same direction and place another stake D. Now walk at right angles to BD until A and C are in line, then place a stake E. The width of the river is five times the distance between D and E. Draw a diagram showing this and explain why it works.

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  1. I assume you drew it.
    Now angle ABC = angle EDC (both right angles)
    and Angle ACB = angle ECD (opposite angles)
    By the way that means angle BAC=angleDEC because they are complementary to equal angles
    Therefore I claim the triangle CDE is similar to triangle CBA
    Therefore AB/BC=DE/DC because they are corresponding parts of similar shapes
    so
    AB/5 = DE/1
    or
    AB = 5 DE
    So if I measure DE I know AB without swimming

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  2. Here is a way to find (roughly) the width of a river without crossing it.
    Place a stake B on one bank opposite a landmark A on the other bank. Walk a distance of 5m along the bank at right abgles to AB and place another stake C. Walk another 1m in the same direction and place another stake D. Now walk at right angles to BD until A and C are in line, then place a stake E. The width of the river is five times the distance between D and E. Draw a diagram showing this and explain why it works.

    ..............A
    --------------*-------------------------
    ..............l.*
    ..............l...*
    ..............l.....*....C
    ..............l.......*../
    --------------*---------*.*D
    ..............B...........*E

    BC = 5, CD = 1

    Triangles ABC and EDC are similar.

    Therefore, AB/DE = BC/CD
    Since, BC = 5 and CD = 1, AB = 5DE.

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