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Browse High School Practical Geometry

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Planar Approximation: Latitude and Longitude [04/18/2003]
I am trying to calculate the midpoint between cases of legionella and their nearest neighbor. How can I calculate the distance between two points below which they can be treated as if they were in a plane rather than on a sphere?

A Practical Use for the Orthocenter [03/07/2001]
Does the orthocenter of a triangle have any practical uses?

Pyramid Construction [05/24/1997]
How do you figure out the angles necessary to construct a pyramid out of plywood?

A 'Pyramiddle' Tent Problem [07/12/1999]
Figure out an equation that yields d when values for h and r are inserted.

Radius of an Arch [05/25/1998]
Is there a formula to calculate the radius of a circle given the chord length and the distance from the centre of the chord to the circle?

Ratios and Geometry [10/29/1998]
An airplane flying at 33,000 feet has a visibility of 100 miles. What percent of the total land area to the horizon is visible?

Ratios, Geometry, Trigonometry [06/10/1999]
A homeschool teacher asks for help with triangles, flagpoles, and circles.

Rectangle Needed To Make Cone [9/5/1996]
I want to make a lampshade by rolling a piece of paper into a non-closed cone shape...

Reflective Properties of a Semicircular Mirror [05/16/2000]
What are the reflective properties of a semicircular mirror? Will a ray exit a semicircular mirror parallel to its entry line?

Resolving Pitch and Yaw [02/10/2003]
Is there an equation to find the resultant of pitch and yaw?

Reuleaux Curve Applications [05/25/2002]
What is the Reuleaux curve used for?

Rhumb Lines and Great Circle Routes [09/24/1998]
Can you explain great circles and rhumb lines and how they relate to shortest distances in geometry?

Roof Rafters [02/03/1997]
What is the formula that gives the length of a roof rafter if only the pitch of the roof is known?

Rotating a Plane about a Point in Space [07/03/2004]
Discussion of a method of rotating the three points of a right triangle around a point to align with a given plane in a particular way.

Scanning for Mountains [06/02/1999]
I am standing on a hill scanning the horizon to see a mountain. How high must the mountain be for high-tech optical equipment to be any use?

Segment of an Ellipse [09/06/2001]
We often use horizontal oval tanks for storing drinking water and fuel, and we would like to be able to calculate the contents.

Setting Sun [5/19/1995]
A fellow Naval retiree and I have been discussing whether the sun appears to set faster at the horizon near the equator than it does in the northern latitudes...

Sextant Theorem [05/13/2001]
What mathematical theorem is behind using a sextant, and can it be proved?

Side Length of Octagon Inscribed in Square [9/11/1996]
I have a piece of square plywood (48" on a side) and I would like to cut an octagon out of the middle. What is the side length of the octagon?

Sixteen-sided Window [08/05/1997]
I would like to make a sixteen-sided window for the second floor hallway of my twin girls' playhouse.

Sizing a Connector [06/01/2001]
I have to come up with a specific diameter for anywhere from 2 to 91 diameters that are bunched together. The application is round wires.

Spine Doctoring: Fitting Some Books on a Shelf, Finding a Textbook in Error [02/08/2016]
An adult student and Doctor Peterson go back and forth on a textbook problem about how many books a bookcase can hold. Together, they puzzle over how to interpret the question and how to model the scenario, before ultimately concluding that the textbook authors made a mistake.

Spiral Baffle in a Cylinder [6/24/1996]
We have a cylinder, 48 inches in diameter, to put a spiral baffle inside... What would the radius be?

Surveyor's Formula [06/05/1999]
Can you give me a method to calculate the area of an irregular polygon given all the coordinates of the points?

Swimming Pool Volume [02/28/2002]
What formula would I use to calculate the volume in gallons of a swimming pool 135' x 70' with different depths of 3', 5', 8' and 11'?

Tanker Bearings [06/11/2000]
From ship A, the bearing of an oil tanker is 300 degrees; from ship B, 1000 m due west of A, the bearing of the tanker is 060 degrees. Is the oil tanker the same distance from A as from B?

Tape Measure Markings [8/11/1997]
What is the small diamond on all tape measures that occurs every 19.2 inches for?

Teaching about Bearings [06/08/2000]
What are bearings? Do you have any ideas on how I can present bearings to my math class in an interesting fashion?

Tiling a Floor [06/30/1999]
How many square yards is a 12ft. by 15ft. room? How many 8" x 8" tiles would you need for a 30 sq. ft. room?

Tipped and Partially Filled Frustum [12/14/2003]
A vessel in a plant where I work is the frustum of a cone on its side. A liquid is contained in this section and pours out the end of the cone section, therefore the liquid only takes up a certain portion of the cone's volume. How can I compute the volume of the liquid?

Total Area of Multiple Objects [07/18/2002]
I have 6 windows and want to know the total square feet. Do I compute the areas separately, or add the dimensions and use those to compute the area all at once?

Triangular Garden [03/18/1997]
Find the length of a fence that runs from the right angle to the hypotenuse and separates the garden into two parts of equal perimeter.

Truncating a Square to Get an Octagon [10/13/2003]
I want to make an octagon by cutting the corners off of a square. Where do I make the cuts?

Using Geometry to Make a Roof [8/30/1995]
I'm not a student but a wood worker with a question on solid geometry. I want to know how to calculate the angle on the sides of triangles in order to form a cone shaped (not round but angular) roof.

Variable Volumes in an Oblate Spheroid [12/21/2002]
We need to know how much water is in the tank at any given time.

Volume of a Cylindrical Tank [2/3/1995]
I have to keep an inventory of how much is kept in a farm of tanks outside my school. The tanks are cylindrical, which would be no problem if they were standing on end...

Volume of a Pond [2/1/1995]
I need to have a large pond cleaned at my place of employment. The pond is completely filled with waste material and I would like to know how many cubic yards are in the pond to remove.

Volume of Dirt [09/29/1997]
You have a mound of dirt that is 2 meters high with a bottom radius of 1 meter...

Volume of Liquid in a Cylindrical Tank [05/08/2000]
How can I calculate volume of liquid in a cylinder that's not full and lying horizontally?

Volume of Partially Full Cylinder on its Side [12/31/2001]
I am in charge of ordering fuel for our company, and the way the owner calculates the volume is via a grossly simplified percent full guesstimation...

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