## Introduction

In mathematics, the tangent is a function that describes the relationship between the angles of a triangle and the lengths of its sides. Tangents are important in trigonometry and calculus, because they can be used to calculate the values of other functions, such as sin and cos. The tangent function can be defined in terms of the sine and cosine functions:

tan(x) = sin(x) / cos(x)

This equation can be used to calculate the tangent of any angle, provided that the value of x is known.

## What is the Tangent of a Angle?

The tangent of an angle is the ratio of the side opposite the angle to the side adjacent to the angle. In other words, it is the ratio of the length of the hypotenuse to that of the perpendicular.

## How to Determine the Tangent of a Angle

There are a few different ways that you can determine the tangent of a angle. You can use a calculator, you can use a table, or you can do it manually. Let’s go over each method so that you can choose the one that is best for you.

### Step One: Determine the Angle

The tangent of an angle is the ratio of the length of the side opposite of the angle to the length of the side adjacent to the angle. In order to determine the tangent of an angle, you must first determine the measure of the angle. You can do this by finding the arctangent, which is the inverse function of tangent, or by using a calculator. The arctangent is written as “tan” with a superscript “-1” after it. For example, if you wanted to find the arctangent of 0.5, you would write “tan” with a superscript “-1” after it and then put 0.5 next to it, like this: tan-10.5. This would give you 26.565, which means that the tangent of 26.565 is 0.5.

### Step Two: Determine the Length of the Side

The next step is to determine the length of the side. To do this, you will need to use a ruler or a measuring tape. For example, if the length of the side is 12 inches, then you would write “12” next to the “Length” label. If the length of the side is 13 inches, then you would write “13” next to the “Length” label.

### Step Three: Determine the Tangent of the Angle

To find the tangent of an angle, you need to divide the length of the opposite side by the length of the adjacent side. You can use a scientific calculator to do this, or you can use a tangent calculator . The answer will be in terms of the number itself. For example, if the length of the opposite side is 13 and the length of the adjacent side is 12, then the tangent would be 1.08 (13 divided by 12).

## Conclusion

To find the tangent of a, we simply need to divide the opposite side by the adjacent side. In this case, we would divide 13 by 12 to get 1.08. For b, we would divide 5 by 12 to get 0.42. For c, we would divide 12 by 5 to get 2.4. Finally, for d, we would divide 13 by 5 to get 2.6. Hope this helped!