Question

what I the Tangent of the 30° angle and the Tangent of the 60° angle?​

Answer 1

Answer:

$\tan(30) = \frac{\sqrt 3}{3}$

$\tan(60) = \sqrt 3$

Step-by-step explanation:

Given

The attached triangle

Required

Find $\tan(30)$ and $\tan(60)$

The tangent of an angle is calculated as:

$\tan(\theta) = \frac{Opposite}{Adjacent}$

So, we have:

$\tan(30) = \frac{b}{a}$

This gives:

$\tan(30) = \frac{3}{3\sqrt 3}$

3 cancels out

$\tan(30) = \frac{1}{\sqrt 3}$

Rationalize

$\tan(30) = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}$

$\tan(30) = \frac{\sqrt 3}{3}$

Similarly;

$\tan(60) = \frac{a}{b}$

This gives:

$\tan(60) = \frac{3\sqrt 3}{3}$

3 cancels out

$\tan(60) = \sqrt 3$