# How do you evaluate #tan(cos^-1((2sqrt5)/5))# without a calculator?

##### 1 Answer

Sep 1, 2016

Evaluate the triangle represented by the

#### Explanation:

Starting with the original:

The first thing to do is evaluate

So we are dealing with a triangle with an angle that has adjacent side

We can find the opposite by using the pythagorean theorem:

We know a and c:

Solving for b:

We can now find the tan function: