Tan 60 value

General
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tan 60 value

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LectureNotes said tan 60 value

Answer:
The tan (tangent) of an angle in a right-angled triangle is defined as the ratio of the opposite side to the adjacent side of the angle. The exact trigonometric value of \tan 60^\circ is a fundamental concept in trigonometry.

Trigonometric Definition of \tan 60^\circ :

  1. Understanding Tan for 60 Degrees:

    • For \theta = 60^\circ , the tangent function can be defined using the special properties of a 30-60-90 triangle. In such a triangle, the sides are in the ratio:
      1 : \sqrt{3} : 2

  2. Calculating Tan for 60 Degrees:

    • To determine \tan 60^\circ , consider a right-angled triangle where one of the angles is 60^\circ .
    • In a 30-60-90 triangle, if the shorter leg (opposite the 30^\circ angle) is 1 unit, then the longer leg (opposite the 60^\circ angle) is \sqrt{3} units, and the hypotenuse is 2 units.
    • Therefore,
      \tan 60^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{\sqrt{3}}{1} = \sqrt{3}

Final Answer:
The value of \tan 60^\circ is:

\tan 60^\circ = \sqrt{3}

This detailed explanation should help you understand how the value of (\tan 60^\circ) is derived.