Tangent Trigonometry

The word trigonometry is an origin of two Greek words “trigonon” meaning a triangle and “metron” meaning measurement. Metron means the science, which deals with the measurement of triangles. The familiar trigonometric terms are sine, cosine, tangent, cotangent, secant, cosecant. The tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space
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Definition of tangent trigonometry:

                A function of an acute angle in a right-angled triangle can be defined as the ratio of the opposite side of length and the adjacent side of the length is called tangent. It is expressed by the gradient of a line. Find either sides or angles in a right-angled triangle by using this function.
      
  In Diagram (A) represents the Thangent to curve
 In Diagram (B) represents the tangent of an angle
 In Diagram (c) represents the tangent to a circle.
                       In Right angle triangle Tangent  can be expressed in mathe matical form. If an angle is` theta`
               ` tan theta ` = `(Opposite side)/(adjacent side)`

Tangent trigonometry problems:

Tangent trigonometry problem 1:
          Find the height of the given right-angle triangle.
           
         Solution:
                               tan 30° = `(opposite)/(adjacent)`
                                             = `h/5`                                                                                 we know, tan 30°= `1/ sqrt3 `

                       height  (h) = 5 × tan 30°
                                           = 5 × `1/ sqrt3 `
                                          =  2.886 (approximately)
      So, The height of the right-angle triangle (h) =2.886 cm


Tangent trigonometry problem 2:
           Find the hypotenuse value of the given right-angle triangle. length and height are in centimeter.

                
      Solution:
                                           Tan` theta`   = `(opposite side)/(adjacent side)`
                                                       = `4/3`
                                   Tan `theta` = 1.333
                                            `theta` = tan^-11.333
                                            theta = 53.12°
                  Now the trigonometry relation,  sin` theta` = `(opposite side) / (hypotenuse)`
                                                               sin 53.12° =` 4 / (hypotenuse)`
                                                     hypotenuse (X) =` 4 / sin 53.12 `                                we know sin 53.12° = 0.7999
                                                     hypotenuse (X) = `4 / 0.7999`
                                                     hypotenuse (X) = 5.000
                  So, the hypotenuse value of right-angle triangle is 5 cm.