Right Triangle Rules

I know that most of us had left our learning of geometry and trigonometry far behind, but to know about the right triangle laws, first we have to define and know what is a right triangle or a right angled triangle. A right triangle is a triangle where one of the angles is a right angle that is it is equal to 90º. The right triangle rules find extensive application in the field of engineering, architecture, navigation, electronics and navigation. The sides of the right triangle is 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 its 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.

Right Triangle Rules: Geometry

Pythagorean Theorem
The basic right triangle rule is the 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 right triangle rule can be used to find the length of any one side of the triangle when the other two sides are given.

Side-Angle-Side Rule
According to this rule, if one of the sides of a right angled triangle is congruent to the other side of another right angled triangle, then the two triangles are said to be congruent.

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

Angle-Angle-Side Rule
According to this rule, 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 right angle than it is said that the two triangles are congruent.

Right Triangle Rules: Trigonometry

The right triangle rules can be used to find any unknown length of the sides and angles of a right triangle by using trigonometric functions. First consider the unknown angle to be A. In a right triangle the trigonometric ratios are defined in the following way. 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 length 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 it has extensive application in navigation, aeronautics and mechanical and electronic engineering.

The right angle triangles can also be of two types. One where the other two angles of the right angled triangle is equal to 30º and 60º and the other where the both the angles of a right angled triangle is equal to 45º. The special right triangle rules are that in a 30-60-90 triangle the length of the hypotenuse is twice the length of one sides and in a 45-45-90 triangle the two sides other than the hypotenuse are equal in length. So these were the right triangle rules that has many wide applications.