# $\tan{(60^°)}$ value

$\tan{(60^°)} \,=\, \sqrt{3}$

The value of tangent in a sixty degrees right triangle is called the tan of angle sixty degrees.

## Introduction

The tangent of angle sixty degrees is a value that represents the ratio of lengths of opposite to adjacent sides when the angle of a right triangle equals to sixty degrees.

In the Sexagesimal system, the tangent of angle sixty degrees is written as $\tan{(60^°)}$ in mathematical form. The exact value for the tan of angle sixty degrees is square root of three. In trigonometry, it is written in the following mathematical form.

$\tan{(60^°)} \,=\, \sqrt{3}$

The value of tangent sixty degrees is an irrational number and its value is written in the following decimal form.

$\implies$ $\tan{(60^°)} \,=\, 1.7320508075\cdots$

$\implies$ $\tan{(60^°)} \,\approx\, 1.7321$

In mathematics, the tangent of angle sixty degrees can also be written in two other forms.

### circular system

The tangent of sixty degrees is written as the tan of quotient of pi by three radian on the basis of circular system. So, it can be written in mathematical form as $\tan{\Big(\dfrac{\pi}{3}\Big)}$.

$\tan{\Big(\dfrac{\pi}{3}\Big)} \,=\, \sqrt{3}$

### Centesimal system

According to the centesimal system, the tan sixty degrees is expressed as tangent of angle sixty six and two third grades and it is written as $\tan{\Big(66\frac{2}{3}^{\large g}\Big)}$ mathematically.

$\tan{\Big(66\dfrac{2}{3}^g\Big)} \,=\, \sqrt{3}$

#### Proofs

The exact value of tangent of sixty degrees can be proved in three different types of mathematical methods.

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