How to measure the height of a mountain using trigonometry?

In this lesson, you can learn to calculate the height of a mountain without any climbing on the mountain. It is very simple and easy. First of all, you want to find only two measuring instruments for this experiment. They are theodolite and any an instrument for measure the distance.

First, you want to choose two points which are on the horizontal line as shown in the fig.  Observer gets the first reading of ascent angle of the point of D (α)  by using the theodolite when he is at the point A. Next, observer goes the distance(AB) From A to B towards the mountain. AB distance should be too long otherwise we can’t get the accurate value for the h because when AB is getting small, the error is getting bigger. At point “B” do same to get the ascent angle fo D(β). Every time we want to minimize errors when doing the experiment.

The α and β are measured by a theodolite. x is measured by any distance meter.    we don’t want to measure the z. Now applying these value to the above equation we can calculate the h.

Calculate the height of the mountain by the equation when readings are in (degrees, minutes, seconds) and meters.

After getting readings for α, β and the value for x. Please input that values into the following relevant text boxes and do the calculation quickly.

α = degrees, minutes, seconds
β = degrees, minutes, seconds
x = meters
to get the answer = meters

Calculate the height of the mountain by the equation when readings are in radians and meters.

If your readings are in radians and meters you can enter the value for α, β, and the x.

α = radians, β = radians, x = meters
to get the answer = meters

Optional Note1: If you want to Convert (degrees, minutes, seconds) to (degrees, decimals) you can do that following equation. An example is done for you. α = 290  30′   14″   = 29 + 0.5 + 0.0038888888888889 = 29.50388888888889 Convert (degrees, minutes, seconds) to (degrees, decimals):

degrees minutes seconds
Answer in (degrees, decimals) = degrees

Optional Note2: Convert (degrees, minutes, seconds) to radians, Input value for θ.

θ = degrees, minuites, seconds
Answer = radians

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