Right-Angled Triangles And Pythagoras Property

Right Angled Triangle

A right-angled triangle is a triangle which has one of its angles as 90° and the side opposite to that angle is the largest leg of the triangle which is known as Hypotenuse .The other two sides are called Legs.

Pythagoras theorem

In a right angle triangle,

(Hypotenuse)2 = (base)2 + (height)2

The reverse of Pythagoras theorem is also applicable, i.e. if the Pythagoras property holds in a triangle then it must be a right-angled triangle.

Example

Find the value of x in the given triangle if the hypotenuse is 5 cm and height is 4 cm.

Solution

Given:

Hypotenuse = 5 cm

Height = 4 cm

Base = x cm

(Hypotenuse)2 = (base)2 + (height)2

52 = x2 + 42

x2 = 5– 42

x2 = 25 – 16

x = 9

x = 3 cm

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