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If three different sides x, y, z of a triangle have three different angles α, β, γ; x + y > z is the inequality and angles α + β + γ = 180°, which is the addition of all the three angles. If γ is a right-angled triangle (i.e., γ = 90°), then the value of the triangle can be calculated using the Pythagoras Theorem (i.e., x² + y² = z²). There are certain trigonometric relationships that involve trigonometric functions as:
Question: A person is observing a tree of 55-foot height. As per his calculation, the pole has a shadow of 23 feet in length. Calculate the angle of the sun's elevation from the shadow's tip?
Solution: Let 'a' as the angle of sun's elevation, then
tan a = 55/23 = 2.391
take tan on the other side i.e., a = tan-1(2.391)
or a = 67.30 degrees
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Trigonometry is mainly divided into two parts which work on different entities or available data regarding different planes or surfaces. These two types of Trigonometry are mentioned below:
Plane Trigonometry is defined as the set of methods and abbreviations used to calculate different angles and side lengths of a two-dimensional plane. It is based on two side coefficients (x, y).
Spherical Trigonometry is much different from the previous one because its abbreviations are used to calculate the various related aspects of a 3D plane also known as three-dimensional Plane Trigonometry. In spherical Trigonometry there mainly three coefficients are used which are (x, y, z).
Trigonometry and Trigonometric functions are used by many data experts in different fields in order to observe wave formed data such as astronomy to determine the huge distances, sides, surface areas and etc, in radiations and wave engineering, in data sciences, in electronics and electromechanics, architecture, seismology, phonetics, etc.
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