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# M3.4.3

Identifies the source of any discrepancy between an estimate and a calculated answer.

### Estimating Planar Areas Using Analogue Methods

A method to estimate planar areas for simple or complex shapes is described. The method relies on the use of weighing the area of interest and using proportional constructs.

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### When a Ruler Is Too Short

Surveyors are often seen in the middle of the street making careful measurements of angles with their transits, and distances with their steel tapes. For points than can be easily reached, such a survey is convenient. But when the target is inaccessible – a mountain summit or a distant star – known distances can be combined with measured angles to determine a distance or altitude. The method relies on parallax, the way an object appears to move, relative to a more distant background, when viewed from different angles.

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### Pilots, Airplanes, and the Tangent of Three (3) Degrees

When approaching an airport, pilots must learn to maneuver their aircraft visually, so that a stabilized approach to the runway can be flown at a constant approach angle. Precise approach planning insures a smooth transition to a landing within the Touchdown Zone (1) of the runway. Pilots must sometimes execute visual approaches that are varied in size, shape, and angle based upon a variety of factors such as: other aircraft, obstructions, noise abatement, or prevailing weather conditions. The standard approach angle however, is 3&deg;.

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### Dream Job

Many people dream of becoming millionaires these days. In order to make this dream come true, people play the stock market, play the lottery, and appear on television game shows designed for this purpose. Counting on the stock market requires placing money at risk and playing the lottery involves playing against the odds. And honestly, the television programs place contestants in the risky position of looking foolish by missing an easy question in front of millions of viewers.

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