# Caculatetan (θ)

θ angle

tan(θ)

In a right angled triangle, Tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

## Formula

To find the Tangent of a given angle θ , use the following formula.

## Calculating Tan of an Angle

The tangent (tan) of an angle in a right triangle is a trigonometric function that represents the ratio of the length of the opposite side to the adjacent side. It is an important function in trigonometry, often used to find unknown side lengths or angles in right triangles.

The tangent of an angle \( \theta \) is defined as:

\( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

where:

**opposite**is the length of the side opposite to angle \( \theta \).**adjacent**is the length of the side adjacent to angle \( \theta \).

### Example 1

Let's calculate the tangent of a 30-degree angle:

In a right triangle, if the angle \( \theta = 30^{\circ} \), the opposite side is half the length of the hypotenuse, and the adjacent side is \( \sqrt{3} \) times half the length of the hypotenuse. So, the tangent of 30 degrees is:

\( \tan(30^{\circ}) = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3} \approx 0.577 \)

### Example 2

Consider another example with a 45-degree angle:

In a right triangle, if the angle \( \theta = 45^{\circ} \), the opposite side and the adjacent side are of equal length. So, the tangent of 45 degrees is:

\( \tan(45^{\circ}) = 1 \)

These examples demonstrate how to calculate the tangent of an angle manually, showing the importance of understanding the trigonometric function tangent in various mathematical and practical applications.