Elevation can be simply described as a particular height above a given reference point in layman's language point of view. However, the theories and mathematical formulas involved in the calculation of elevations especially in trigonometric studies provide a different meaning to it through the use of trigonometric ratios such as the cosines, tangents, and sines. Trigonometric ratios provide the easiest and most convenient hypothetical approach to the calculation of elevations.
Figure 1
From the illustration in figure 1 above, the right angled triangle is represented by vertices A, B, and C respectively. The elevation of the right-angled triangle is represented by the symbol ϴ which automatically provides the angle of the elevation of the right angled triangle . Similarly, line AB which is directly opposite to the angle of elevation is called the opposite, the line AC which is below the angle of elevation is described as being adjacent to the angle of elevation whereas the inclined plane BC above the angle of elevation is referred to as the hypotenuse. It is important to understand the meaning of these sides since they are the main basics which constitute the trigonometric ratios. Through different theories and mathematical formulas of calculating elevations, the angle of elevation can be calculated using the following trigonometric ratios.
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Sine
ϴ
=
=
Tangent
ϴ =
=
Cosine
ϴ =
=
Thereafter, the value of the angle of elevation of a particular figure or plane is given by determining the respective inverse of the calculated trigonometry ratios such as;
ϴ =
,
or
The height or the elevation of a particular object can be established as follows using trigonometric ratios. Since
=
then the height of the right-angled triangle can be determined by manipulating the formula by multiplying both sides by BC.
Height AB =
(BC) or
Height AB =
(AC).
