What is the value of $\tan 30^{\circ }$?

Step-by-step solution

1. Recall the $30^{\circ }$–$60^{\circ }$–$90^{\circ }$ triangle: sides are $1$, $\sqrt{3}$ and $2$ (opposite $30^{\circ }$, opposite $60^{\circ }$, hypotenuse).
2. For $30^{\circ }$, opposite side = $1$, adjacent side = $\sqrt{3}$.
3. Use $\tan \theta =\frac{\text{opposite}}{\text{adjacent}}$, so $\tan 30^{\circ }=\frac{1}{\sqrt{3}}$.
4. Rationalise the denominator: $\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}$.

Concept tested: Standard trigonometric values

Published 25 August 2026 · How this solution was prepared and checked

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