Question

trigonometric ratios
determining a tangent ratio
what is the value of tan(60°)?

Explanation:

Step1: Recall tangent - ratio formula

The formula for the tangent of an angle in a right - triangle is $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For a $60^{\circ}$ angle in a $30 - 60-90$ triangle, if the shorter leg (opposite the $30^{\circ}$ angle) is $a$, the longer leg (opposite the $60^{\circ}$ angle) is $a\sqrt{3}$ and the hypotenuse is $2a$.

Step2: Use the special - triangle values

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

Answer:

$\sqrt{3}$