A closed figure that is formed by three line segments such a way that no two segments meet each other more than once. This two dimensional figure is known as a triangle. The point where the two segments meet each other is known as the vertex. There are three angles and three sides for a triangle.

Triangle Types (Read more)

They can be classified based on the angles and sides.

There are three types based on sides. They are scalene, Isosceles and equilateral.

There are three types based on angles. They are acute angled, right angled and obtuse angled.

In this article we shall learn more about a right triangle.

What is a Right Triangle? (Read more)

It is a triangle in which one of its angle measures 90 degrees. It cannot have two right angles because the sum of two right angles is 180 degrees whereas the sum of three angles of a triangle is 180 degrees. From this we understand that the other two angles of a right angled triangle are acute angles (measure of the angles is between 0 and 90)

In a right triangle the side that is opposite the angle 90 degrees is known as hypotenuse. The other two sides that contain the right angle are known as the legs of the triangle.

There is a famous rule that connects all these three sides. That is square on the hypotenuse is equal to the sum of the squares of the two legs. This is used to find the unknown side while the two are given.

Example: 1

Find the unknown side of a right triangle whose hypotenuse (Read more) is 25 cm and one of its leg measures 7 cm.

Solution:

We know that (hypotenuse)2 = (Leg 1)2 + (Leg 2)2

Here Hypotenuse = 25 cm and let Leg 1 = 7 cm, Leg 2 = x Substituting these values in the above formula we get

(25)2 = 72 + x2

625 = 49 + x2

625 – 49 = x2

576 = x2

x = 24

Therefore, the unknown side = 24 cm

Special Cases:

When the angles measure 30 degrees, 60 degrees and 90 degrees. That is the angles are in the ratio 1: 2:3. In this the sides of such a triangle are in the ratio 1: √3 : 2.

The other special case is when the angles measure 45 degrees, 45 degrees and 90 degrees. That is the angles are in the ratio 1: 1: 2. In this the sides are in the ratio 1: 1: √2. This is also known as isosceles right triangle.

Let us see few examples based on the special cases

Example:

Find the missing sides of the triangle given below.

Solution:

The given three sided figure a special case. Here we see that the angles are in the ratio 1: 2: 3. Therefore the sides are in the ratio 1: √3 : 2.

To find y, we do 1: 2 = 6: y

That is y = 12 cm

To find x, we do 1: sqrt(3) = 6: x

That is x = 6√3 cm

Example:

Find the missing sides of the triangle given below.

Solution:

The given three sided figure a special case. Here we see that the angles are in the ratio 1: 1: 2. Therefore the sides are in the ratio 1: 1: √2.

To find a, we do 1: 1 = 3: a

That is a = 3 cm

To find b, we do 1: √2 = 3: b

That is b = 3√2 cm