Pythagorean Theorem is a very important theorem used in Trigonometry. It gives a relationship between the sides of a right triangle. A Greek philosopher Pythagoras was the founder of Pythagorean Theorem.
Introduction to Pythagorean Theorem:
Pythagorean Theorem describes a relationship between the longest side of the right triangle and the remaining smaller sides.
Statement: In right triangle, the square of longest side (hypotenuse) is equal to the sum of square of the remaining two sides.
Explanation of Pythagorean theorem:
In a right-angled triangle,
Let ‘a’ = adjacent side, ‘b’ = opposite side, ‘c’ = hypotenuse
Using Pythagorean Theorem,
(Hypotenuse) 2 = (adjacent side) 2 + (opposite side) 2.
Examples of Pythagorean Theorem :
Ex 1: Find the hypotenuse of the right triangle when the adjacent and opposite sides of the right angled triangle is 4cm and 3cm.
Sol: The triangle given is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: 42 +32 = x2
Step III: 16+9 =x2
Step IV: 25 = x2
Step V: x = 5
The hypotenuse side of the triangle is 5cm
Ex 2: Find the adjacent side of the right triangle when the hypotenuse and opposite sides of the right angled triangle is 10cm and 6cm.
Sol: The given triangle is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: x 2 +62 = 102
Step III: 100-64 =x2
Step IV: 36= x2
Step V: x=6
The hypotenuse side of the triangle is 6cm
Ex 3: Find the opposite side of the Right Triangles Trigonometry when the hypotenuse and adjacent sides of the right angled triangle is 10cm and 5cm.
Sol: The given triangle is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: 52+ x 2 = 102
Step III: 100-25 =x2
Step IV: 75= x2
Step V: x=8.7
The hypotenuse side of the triangle is 8.7cm
These examples are used to learn online pythagorean theorem.
Introduction to Pythagorean Theorem:
Pythagorean Theorem describes a relationship between the longest side of the right triangle and the remaining smaller sides.
Statement: In right triangle, the square of longest side (hypotenuse) is equal to the sum of square of the remaining two sides.
Explanation of Pythagorean theorem:
In a right-angled triangle,
Let ‘a’ = adjacent side, ‘b’ = opposite side, ‘c’ = hypotenuse
Using Pythagorean Theorem,
(Hypotenuse) 2 = (adjacent side) 2 + (opposite side) 2.
Examples of Pythagorean Theorem :
Ex 1: Find the hypotenuse of the right triangle when the adjacent and opposite sides of the right angled triangle is 4cm and 3cm.
Sol: The triangle given is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: 42 +32 = x2
Step III: 16+9 =x2
Step IV: 25 = x2
Step V: x = 5
The hypotenuse side of the triangle is 5cm
Ex 2: Find the adjacent side of the right triangle when the hypotenuse and opposite sides of the right angled triangle is 10cm and 6cm.
Sol: The given triangle is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: x 2 +62 = 102
Step III: 100-64 =x2
Step IV: 36= x2
Step V: x=6
The hypotenuse side of the triangle is 6cm
Ex 3: Find the opposite side of the Right Triangles Trigonometry when the hypotenuse and adjacent sides of the right angled triangle is 10cm and 5cm.
Sol: The given triangle is a right angled triangle , it obeys pythagorean theorem
Step I: (adjacent side)2+(opposite side)2= (hypotenuse side)2
Step II: 52+ x 2 = 102
Step III: 100-25 =x2
Step IV: 75= x2
Step V: x=8.7
The hypotenuse side of the triangle is 8.7cm
These examples are used to learn online pythagorean theorem.
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