## tan 30°

### The tangent of 30 degrees, written as tan 30°, is an important trigonometric function that represents the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle

The tangent of 30 degrees, written as tan 30°, is an important trigonometric function that represents the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle.

To find the value of tan 30°, we can use either a unit circle or the special right triangle with angles of 30°, 60°, and 90°.

Using the unit circle approach, draw a circle with a radius of 1 unit. Place the angle of 30 degrees in the first quadrant. The terminal side of the angle (the side that intersects the circle) will form a right triangle with the radius of the circle and the x-axis. Since the radius is 1 unit, the side opposite the angle is 1/2 (half of the radius), and the side adjacent to the angle is √3/2 (the other leg of the right triangle).

Now, we can write the formula for tangent as tan θ = opposite/adjacent. Plugging in the values, we get tan 30° = (1/2) / (√3/2). To simplify this expression, we multiply the numerator and denominator by the conjugate of the denominator (√3/2), which yields:

tan 30° = (1/2) * (2/√3) = 1/√3 = √3/3

Therefore, the value of tan 30° is √3/3, which is approximately 0.577.

##### More Answers:

Understanding and Evaluating the Tangent Function | Finding the Value of Tan 60°Understanding the tangent function in trigonometry | Exploring the value of tan 45° and its significance in right triangles

Cosine of 60 Degrees | Definition, Calculation, and Example