Characteristics of Right Angle Triangle

Triangle is a basic shape in geometry. A right triangle means 90 - degree angle that is one angle is right angle. It also called as right angled. It shows the relations between the sides and angles of a right triangle and it is the basic concept of trigonometry. The opposite side of the right angle is known as hypotenuse. The adjacent side to the right angle is known as legs or sometime known as catheters. This phenomenon is the basis of Pythagorean triangle theorem. This theorem states that the length of all three sides of a right triangle are integer and the side length are known as Pythagorean triple.

The basic principle properties of a right triangle are area, altitude, Pythagorean Theorem, inradius and circumradius. First we discuss about area of a right triangle. Area of a right triangle is equal to the one half of the base multiplied by the corresponding height. It is true for all right angled triangles. In a right triangle from the two legs if one leg is taken as a base then other leg is taken as height. So in other way we can say that area of a right triangle is one half of the product of the two legs means one half products of base and height. Mathematically suppose in a right triangle two legs are (a) and (b) and hypotenuse is (c) then formula for the area of a right triangle is expressed as [A=(1/2 ab)].

For finding area of a right triangle we have to calculate perimeter also. The formula we can see above. Suppose in a right triangle two legs (a=5) and (b=12) where a is base and b is height. Hypotenuse (c=13) is given. We know the formula area of a right triangle so we substitute all the values in formula. Finally we get area= (1/2 *5*12) = (1/2*60) =30 and unit of right angle triangle is square meter or square centimeters.

Similarly we can find surface area of a right triangle.  Formula for surface area of right angle triangle is [Area (A) =bc/2] where (a=√b^2+c^2), (b=√a^2-c^2) and (c=√a^2-b^2). Suppose for above problem we have to find surface area. We substitute all the values in formula that is (A=12*13/2).
From the right angle triangles we also find the Pythagorean Theorem. It is very useful in all parts of mathematics. It states that in any right angle square of hypotenuse is equal to sum of square of base and square of height that is (c^2=a^2+b^2).