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Geometry and Topology

Measurement of a parallelepiped brick's diagonal

You have a brick of parallelepiped shape. You need to measure its diagonal (a distance between two opposite vertexes remote to the maximum). You have in your disposition a ruler and a rectangular edge of the plane surface (of the table, for example). What should you do to measure the diagonal if 1. You have also a pencil to ma

Geometry: Angles

Suppose <ABC and<CBD form a linear pair, <CBD and <DBE form a linear pair, and m<CBD=30. A. Draw a figure representing these angles. B. Write a paragraph proof showing that <ABC=<DBE.

Rigid Pentagonal Prism

How many lines would you need to add to a pentagonal prism anchored to the ground to make it rigid?

Calculating the departure angles.

For a gun where the departure angle 'Beta' and the distance "D" in meters that the projectile travels are related by D=1250sin2Beta. Find which departure angles can be used to hit a target 800 meters away.

Finding Apothems

Please explain how to find the apothem, especially in regards to 45-45-90 and 30-60-90 triangles.


What is this symbol and what does it mean? See attachment.

Proving that h meets line AD.

Assume that AC < w, A-B-C, and D is a point on AC line segment. Let h be a ray with endpoint C such that h meets BD line interior. Prove that h meets AD line.

Finding the Volume of a Fish Tank (filling the fish tank with sand)

I need an equation or equations to help me find out how many pounds of sand I will need to fill my fish tank and so I can determine how much it will cost me. The tank measures 71 inches in length and 18 inches in width. I want to know how much sand I will need for a 3, 4, 5, and 6 inch base.