Question

what is the value of tan(60°)?

Explanation:

Step1: Recall tangent - ratio definition

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For an angle of $60^{\circ}$ in a $30 - 60-90$ triangle, if the shorter leg (adjacent to the $60^{\circ}$ angle) is $x$ and the longer leg (opposite to the $60^{\circ}$ angle) is $\sqrt{3}x$.

Step2: Calculate $\tan(60^{\circ})$

$\tan(60^{\circ})=\frac{\text{opposite side to }60^{\circ}}{\text{adjacent side to }60^{\circ}}$. In a $30 - 60 - 90$ triangle, if the side adjacent to the $60^{\circ}$ angle is $1$ and the side opposite to the $60^{\circ}$ angle is $\sqrt{3}$, then $\tan(60^{\circ})=\sqrt{3}$.

Answer:

$\sqrt{3}$