What I the Tangent of the 30° angle and the Tangent of the 60° angle?

Question

asked Feb 13, 2022 198k views

1 Answer

Noble Eugene · Answer 1 · 2022-02-17T21:18:03+0000

Answer:

$\tan(30) = (\sqrt 3)/(3)$

$\tan(60) = \sqrt 3$

Explanation:

Given

The attached triangle

Required

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

The tangent of an angle is calculated as:

$\tan(\theta) = (Opposite)/(Adjacent)$

So, we have:

$\tan(30) = (b)/(a)$

This gives:

$\tan(30) = (3)/(3\sqrt 3)$

3 cancels out

$\tan(30) = (1)/(\sqrt 3)$

Rationalize

$\tan(30) = (1)/(\sqrt 3) * (\sqrt 3)/(\sqrt 3)$

$\tan(30) = (\sqrt 3)/(3)$

Similarly;

$\tan(60) = (a)/(b)$

This gives:

$\tan(60) = (3\sqrt 3)/(3)$

3 cancels out

$\tan(60) = \sqrt 3$