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Expert: - 4/30/2011


Question
Sometimes it is impossible to get to the base of the tall object being measured, therefore it is not possible to measure the immediate horizontal distance when you are standing in front of the object.

You have been asked to determine the height of Mount Warning.  You are unable to directly access the base of the mountain.  Using theory, formulae or any relevant examples or questions that you have covered in class, describe a method that could be used to find the height of Mount Warning, using a clinometer to measure the angles of elevation.

You must also include a labelled diagram representing the method you described above.

Answer

Mountain
Using the drawing, the points A and B are two points on the ground.
The angle between horizontal and the top of the mountain is measured at each of these points.

The distance between A and B is known, and is d.

It can then be said that (x+d)/c = ctnA and x/c = ctnB.
This gives two equation with two unknowns.

Since from the 2nd equation, it is known that x = c*ctnB,
this can be put in the 1st equation for x.
That gives ctnA = (c*ctnB + d)/c.

Multiplying both sides by c gives c*ctnA = c*ctnB + d.

Subtract off c*ctnB from both sides and get c*ctnA - c*ctnB = d.

This is the same as c(ctnA - ctnB) = d.

Dividing both sides by (ctnA - ctnB) gives c = d/(ctnA - ctnB).

Since angles A and B can be measured and the distance d determined, c can then be calculated.  

Scott A Wilson

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