# Law Of Tangent Formula

## Law of tangent formula

A right triangle’s sides and angles are related by the Law Of Tangent Formula, a trigonometry rule. The relationship between the sum and differences of a triangle’s sides and angles is given by the Law Of Tangent Formula. Any triangle with two sides and one angle or one side and two angles can have the remaining pieces found using the tangent rule. Much like the sine and cosine laws, the Law Of Tangent Formula has numerous applications in various mathematical computations.

## Introduction to Law of Tangents

The right triangle is the foundation of trigonometry. Thus, one of the relationships in that right triangle is defined by the tangent. The ratio of the opposite side to the adjacent side of a specific right triangle angle is the relationship that the tangent defines.

The side opposite the right angle is always the hypotenuse, which never changes. Depending on the angle selected, the adjacent and opposite sides will change. The opposite and adjacent sides would be reversed if the other is chosen, an unmarked angle. The neighbouring side would switch to the opposing side, and vice versa. Finding the hypotenuse is necessary in order to find the tangent. The longest side of a right triangle is typically the hypotenuse. The angle of concern needs to be identified next. There are only two angles available. The adjacent side is the side that is not the hypotenuse and is located next to a selected angle. The opposite side is the side that is opposite the selected angle. After labelling the sides, proceed to take the proper ratio.

## Tangent Rule Explanation

The rules of tangent describe the difference and sum of sides of a right triangle as well as the tangents to half of the difference and sum of corresponding angles (Law of Tan). It shows the connection between the tangent of two triangle angles and the lengths of the opposing sides. Like the laws of sines and cosines, the Law Of Tangent Formula can be applied to a non-right triangle and is just as useful. If two angles and one side or two sides and one angle are given, the congruence of triangles theory can be used to determine the remaining triangle segments. Side-angle-side (SAS) and angle-side-angle are these (ASA).

## Law of Tangents Proof

The ratio of the sum and difference of any two sides of a triangle is equal to the ratio of the tangent of half the sum and tangent of half the difference of the angles opposite the respective sides.

## Law of Tangent Formula

A right triangle’s relationship between its sides and angles is described by the trigonometric law of tangents. The relationship between the sum and differences of a triangle’s sides and angles is described by the tangent rule. Any triangle with two sides and one angle or one side and two angles can be divided into its component parts using the tangent rule. Like the sine and cosine laws, the law of tangents has a variety of mathematical uses. All the important formulas specific to tangent rule should be revised by students. There are important questions associated with the Law Of Tangent Formula. Solving them is important for boosting the confidence level of students.

### Fun Facts

In the 13th century, the Persian mathematician Nasir al-Din al-Tusi developed the law of tangents for triangles. He gave an explanation of the law of tangents for spherical triangles.

The spherical law of tangents states that the tangent of the difference between two sides and the tangent of their sum is equal to the tangent of the half of the difference between their opposing angles and the tangent of half of their sum.

### Conclusion

The sum and difference of any two triangle sides and their corresponding angles are related by the rule of tangent. According to the tangent rule, the ratio of any two triangle sides’ difference and sum is equal to the ratio of their opposite sides’ angles’ tangent of half their difference and sum. When two sides, an angle, or two angles, a side are given, the rule of tangents can be used to determine the unknown portions of the triangle.