Evaluate tan 30° without using a calculator by using ratios in a reference triangle.

Step-by-step explanation:

hey there,

< You are going to need to memorize the reference triangles for this. There are two of them: one has the angles of 45, 45, and 90 and the other has the angles 30, 60, and 90. Each side also have a value. There's ways to memorize them, so make sure you do that so you can solve these kinds of questions in the future!

Below, I attached a reference triangle for 30, 60, and 90. Here we are finding tan 30. tan = O/A. The angle we are using here is 30, so let's think about the adjacent, opposite, and hypotenuse sides.

tan =

Obviously, you can never have a square root in the denominator so bring it to the numerator and continue solving:

The final answer of tan30 is square root of 3 divided by 3. >

Hope this helped! Feel free to ask anything else.

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1