Question

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

Answer 1

`\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`