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Monday, December 12, 2011

Measure Remote Object Height by Sine Formula

If it is required to measure the height of an object from a certain distance without the need to go to that object, and the distance from the observer to the object is also not known. With only a protractor and distance measuring tool, these measurements can be calculated. Distance from observer to objects can also be calculated, without the need to go to the object.

This method uses a sine formula:

With simple input or measured data, that are:
at point A, the angle of the horizontal plane to the object = a
horizontal distance from point A to point B = L
at point B, the angle of the horizontal plane to the object = b

Formulas for calculation are:
straight distance from point A to object = b = sin 
b x L / sin b g = sin x L / sin (180 -a - b)
height of the object is = T = sin 
a x b
horizontal distance from point A to O or object base = AO = (b2 - T2) 1 / 2

To get accurate results, the distance A to B or L should be as long as possible, and the line L is an imaginary straight line through A and point O or base of object. The surveyors in the field of geodesy are using a Theodolite or Total Station, which is an instrument capable of measuring distances up to 1500 meters with an accuracy of 1.5 mm by a microwave or infrared device, and it is able to measure angles with an accuracy of nearly 0.5 seconds, so it obtains very accurate measurement results. 

The attached Excel document has a formula to calculate the height,and distance to an object.
Distance units and are used can be anything, eg: feet, miles, feet, mile, etc..
For the measurement of angles, always use the unit degrees.

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