The formula set for the right triangle includes the area of the right triangle formula and also formulas for the perimeter and hypotenuse length formula.

In geometry, you learn about various forms of figures and how their properties define them differently from one another. Among these are triangles. A triangle is a closed figure-a polygon-made up of three sides. It has three vertices and its three sides close in three interior angles of the triangle. The sum of the three interior angles of a triangle is = 180 degrees.

The most common types of triangles that we learn are equilateral, isosceles, scalene, and right-angled triangles. In the following part, we discuss the formula related to the right triangle, also known as right-angled triangle formulas.

Right Triangle

A right triangle is the one in which the measure of any one of its interior angles is 90 degrees. It is to be noted here that since the sum of interior angles in a triangle is 180 degrees, only 1 of the 3 angles can be a right angle.

If the other two angles are equal, that is 45 degrees each, then it becomes an isosceles right-angled triangle. However, if the other two angles are unequal, then it is a scalene right-angled triangle.

The most important use of right-angled triangles arises in trigonometry. In fact, the relation of the angles of this triangle to its sides is the basis for the building up of trigonometry.

Area of a right triangle – Formula

It is the region covered by its boundaries or within its three sides area of a right triangle.

The formula for finding the area of a right triangle, governed by where both b and h represent base and height of the triangle, respectively, is given below,

Perimeter of a right triangle – Formula

The perimeter of a right triangle is a distance covered by its boundary or the sum of all its three sides .

The formula for determining the perimeter of a triangle is given by:

Perimeter of a right triangle = a + b + c

Where a, b and c are the measure of its three sides .

Hypotenuse of a right triangle - Formula

A right triangle is a triangle with three sides: the base, the perpendicular and the hypotenuse. The longest side of right triangle is the hypotenuse. Pythagoras Theorem gives the relationship between the three sides of a right-angled triangle. Hence, if we are given the measure of two of the three sides of a right triangle, we can use the Pythagoras Theorem to obtain information about the third side.

In the figure above, ∆ABC is a right-angled triangle that is right-angled at B. The longest side opposite to the right angle, is called the hypotenuse of the triangle. In ∆ABC, AC is the hypotenuse. Angles A and C are the acute angles. We refer to the other two sides-than the hypotenuse-as the 'base' or 'perpendicular' depending on which of the two angles we choose to take for working with the triangle.

Derivation of Right Triangle Formula

Consider the right-angled triangle ABC, in which the angle B is 90 degrees and AC is the hypotenuse.

Now we turn the triangle over its hypotenuse such that a rectangle ABCD of width w and length l is formed.

You already know that area of a rectangle is given as the product of its length and width, that is, length x breadth.

Hence area of the rectangle ABCD = b x h

You will observe that the area of the right angled triangle ABC is just half the area of the rectangle ABCD.

Therefore, area of a right angled triangle, if its base b and the height are known.

Solved example

Question 1: The length of two sides of a right angled triangle is 5 cm and 8 cm.

Find:

Length of its hypotenuse

Perimeter of the triangle

Area of the triangle

Solution: Given,

One side a = 5cm

Other side b = 8 cm

The length of the hypotenuse is,

Using Pythagoras theorem,

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Right Triangle Formula