$\tan{(18^°)} \,=\, \dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$
The value of tangent function when the angle is eighteen degrees in a right triangle, is called the tan of angle eighteen degrees.
According to the Sexagesimal system, the tan of eighteen degrees is written in mathematical form as $\tan{(18^°)}$.
The exact value of tangent of angle eighteen degrees can be written in the following fraction form.
$\tan{(18^°)} \,=\, \dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$
The value of tan of eighteen degrees is an irrational number and the following is the exact value of tan of $18$ degrees in decimal form.
$\tan{(18^°)} \,=\, 0.3249196962\ldots$
The irrational value of tan of eighteen degrees is considered as $0.3249$ approximately in mathematics.
$\implies$ $\tan{(18^°)} \,\approx\, 0.3249$
The $\tan{(18^°)}$ is written as $\tan{\Big(\dfrac{\pi}{10}\Big)}$ as per circular system, and also written as $\tan{(20^g)}$ as per Centesimal system.
$(1) \,\,\,$ $\tan{\Big(\dfrac{\pi}{10}\Big)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$ $\,=\,$ $0.3249196962\ldots$
$(2) \,\,\,$ $\tan{(20^g)}$ $\,=\,$ $\dfrac{\sqrt{5}-1}{\sqrt{10+2\sqrt{5}}}$ $\,=\,$ $0.3249196962\ldots$
The value of tan of eighteen degrees can be derived in mathematics in two different methods.
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