Mathematics students are likely to hear about the Pythagoras Theorem, which explains the relationship between the sides of a right-angled triangle. It is also sometimes called Pythagorean Theorem. It allows one to determine the length and angle of an unknown side or angle of a triangle. Using the Pythagorean Theorem, we can calculate hypotenuse, base, and perpendicular formulas. A right-angled triangle is said to be a right triangle when the square of its hypotenuse is equal to the sum of the squares of its other two sides. In this case, the sides are called Perpendicular, Base, and Hypotenuse.
A right triangle has three sides with positive integer values, say, a, b, and c, which is squared, also called a Pythagorean triple. The hypotenuse is the longest side since it is opposite to the angle of 90°. Pythagoras is referred to as the father of the theorem by mathematicians worldwide. A right triangle can be created using the Pythagoras theorem if we know its two sides. We can find its third side if we know the other two sides. For example, it can be used to find the drop in elevation of a mountain or determine the distance between an observer and a point on the ground from a tower or building. It is applied in the construction field.
The formula of Pythagoras theorem:
Using Pythagoras Theorem’s definition, the formula reads:
Hypotenuse 2 = Perpendicular 2 + Base 2
C2 = a2 + b2
In the triangle, the side opposite the right angle of 90° is the longest, known as the hypotenuse, since the side opposite the greatest angle is the longest.
Assume you have three squares with sides A, B & C that are mounted on three sides of a triangle with the same sides
By Pythagoras Theorem:
Area of square A + Area of square B = Area of square C
How to find the third side of a right-angled triangle, if you know the other two?
To find, remember the formula given below:
C2 = a2 + b2
Where a, b, and c are the sides of the right triangle.
For example, if the value of a = 6 cm, b = 8 cm, then find the value of c.
We know,
C2 = a2 + b2
C2 = 36 + 64
C2 = 100
C = √100
C = 10
Hence, the third side is 10 cm.
As we can see, a + b > c
6 + 8 > 10
14 > 10
Hence, c = 10 cm is the hypotenuse of the given triangle.
How can you find out if the given triangle is right-angled or not?
We can use the Pythagorean theorem to determine whether or not a triangle is right-angled if the lengths of its three sides are known.
Example: Suppose a triangle with sides 9, 12, and 15 is given.
15 is the longest side.
It also satisfies the condition, 9 + 12>15
We know,
C2 = a2 + b2 …(1)
So, let a = 9, b = 12 and c = 15
First we will solve R.H.S. of equation 1.
a2 + b2 = 81 + 144 = 225
Now, taking L.H.S, we get;
C2 = 15 2 = 225
We can see,
LHS = RHS
Therefore, the given triangle is a right triangle, as it satisfies the theorem.
Pythagorean Theorem can calculate the distance between two straight lines given their measurements. It is used in architecture, woodworking, and other construction works. You can learn more about the right-angled triangle from Cuemath, one of the best online maths tutors for anyone who wants to learn maths.