Question

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

Answer 1

Answer: Root 3 / 3

Step-by-step explanation: Use unit circle trigonometry.

Answer 2

Answer:

$\frac{\sqrt{3} }{3}$

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 = $\frac{1}{\sqrt{3} }$

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

$\frac{1}{\sqrt{3} } = \frac{1}{\sqrt{3} }(\frac{\sqrt{3} }{\sqrt{3} } ) = \frac{\sqrt{3} }{3}$

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

Hope this helped! Feel free to ask anything else.