Question

Find tan 0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.

Answer 1

`(12)/(5)`

Explanation:

In order to find tan of theta, we need to find the side that is opposite of the angle and the side adjacent to the angle.

We are given the side that is adjacent to the angle which is 5.

We are not given the side opposite of the angle.

We can use the pythagorean theorem to find the missing side since we have a right angle.

13 is the hypotenuse and 5 and the missing side are legs so our equation look like

`{5}^(2) + {x}^(2) = {13}^(2)`

`25 + {x}^(2) = 169`

`{x}^(2) = 144`

`x = 12`

so our missing side length is 12.

Now using tan formula,

`(opp)/(adj)`

our exact value is

`(12)/(5)`