Dr. Bob's Skeptical Quiz

Quiz Results - January 2000

 

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Flagpole problem (from first principles?)

Back to: January 2000 Quiz Results

Given the diagram below, we are looking to determine the length of the line AC (=h)

1. Given the angle BCD is right, the line BD can be computed as:

2. The angle ADB, and thus the angle ADE, can be computed as:

3. Lines AB and AD are both radii of the same circle, so the triangle ABD is isosceles on a base BD.

4. Therefore the midpoint of the line BD, designated E, forms a line AE perpendicular to BD, and the two line segments BE and ED are of length:

5. The cosine of the angle ADE is computed as:

6. Restating this equation for h we get:

7. Now substituting some arithmetic (Windows calculator, scientific view):

By Dave Hawley