# Right Triangle Rules You've Probably Forgotten

Rimlee Bhuyan Jun 6, 2019
Right triangle rules have applications in various fields. This write-up expounds the various geometric and trigonometric rules of right angled triangles.
A right triangle is a triangle where one of the angles is a right angle, i.e., it is equal to 90º. Its rules find extensive application in the field of engineering, architecture, navigation, and electronics.
The sides of a Right triangle are known by three different names. The side which is directly opposite to the right angle is called the Hypotenuse and this is the longest of the three sides. The other two sides, which are smaller than the hypotenuse are named depending upon their relation with another angle of the triangle, excluding the right angle.
If the angle that is at the base of the triangle is taken into consideration, then the side opposite to this angle is called the opposite side and the side adjacent to it is called the adjacent side.

## Rules in Geometry

### Pythagorean Theorem

It states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the other two sides of the triangle. This rule can be used to calculate the length of any one side of the triangle when the length of other two sides are known.

### Side-Angle-Side

It states that, if one of the sides of a right angled triangle is congruent with the side of another right angled triangle, then the two triangles are congruent.

### Angle-Side-Angle

According to this rule, if one side and an acute angle of a right angled triangle is congruent to the corresponding side and acute angle of another triangle, then the two triangles are congruent.

### Angle-Angle-Side

It says, if the hypotenuse of a right angled triangle as well as another angle of the triangle, other than the right angle is congruent to the hypotenuse and angle of another triangle then the two are said to be congruent.

## Rules in Trigonometry

These rules can be used to find any unknown length of the sides and angles of a right triangle by using trigonometric functions. There are three basic functions in trigonometry and they are called sin, cos, and tan.
Sine A is equal to the ratio of the length of the opposite side to the length of the hypotenuse of a right triangle. Cosine A is the equal to the ratio of the length of the adjacent side to that of the hypotenuse of a right angled triangle. Tangent A is the ratio of the length of opposite side to the length of the adjacent side of a right angled triangle.
With the help of these ratios, unknown length of sides as well as angles of a right angled triangle can be calculated. Trigonometric ratios are very important and they has extensive application in navigation, aeronautics, mechanical, and electronic engineering.
The right angle triangles can be of these two types. One where the other two angles are of 30º and 60º and the other type where both the angles are of 45º.
The special right triangle rule says that in a 30-60-90 triangle, the length of the hypotenuse is twice the length of one side and in a 45-45-90 type, the two sides other than the hypotenuse are equal in length.