Pythagorean Theorem Formula Hindi or English
Pythagorean Theorem Formula
Pythagorean Theorem is one of the most principal theorems in science and it characterizes the connection between the three sides of a right-angled triangle. You are now mindful of the definition and properties of a right-angled triangle. It is the triangle with one of its angles as a right angle, that is, 90 degrees. The side that is inverse to the 90-degree angle is known as the hypotenuse. The other different sides that are adjacent to the right angle are called legs of the triangle.
(पायथागॉरियन प्रमेय विज्ञान में सबसे प्रमुख प्रमेयों में से एक है और यह एक समकोण त्रिभुज के तीन पक्षों के बीच संबंध की विशेषता है। अब आप एक समकोण त्रिभुज की परिभाषा और गुणों से सावधान हैं। यह एक समकोण के रूप में एक कोण है, जो कि 90 डिग्री है। वह पक्ष जो 90 डिग्री के कोण पर उलटा होता है, कर्ण के रूप में जाना जाता है। दूसरे अलग-अलग पक्ष जो समकोण के समीप होते हैं, उन्हें त्रिभुज के पैर कहा जाता है।)
The Pythagoras theorem, otherwise called the Pythagorean theorem, expresses that the square of the length of the hypotenuse is equivalent to the total of squares of the lengths of other different sides of the right-angled triangle. Or on the other hand, the aggregate of the squares of the two legs of a right triangle is equivalent to the square of its hypotenuse.
(पाइथागोरस प्रमेय, जिसे अन्यथा पाइथागोरस प्रमेय कहा जाता है, व्यक्त करता है कि कर्ण की लंबाई का वर्ग समकोण त्रिभुज के अन्य विभिन्न पक्षों की लंबाई के वर्गों के कुल के बराबर है। या दूसरी ओर, एक दाहिने त्रिभुज के दो पैरों के वर्गों का कुल इसके कर्ण के वर्ग के बराबर है।)
Pythagoras Theorem FormulaLet us consider one of the legs on which the triangle rests as its base. The side inverse to the right angle is its hypotenuse, as we definitely know. The staying side is known as the opposite. In this way, numerically, we speak to the Pythagoras theorem as:
(पाइथागोरस प्रमेय सूत्र हमें उन पैरों में से एक मानते हैं जिन पर त्रिकोण अपना आधार बनाता है। दाहिने कोण पर उलटा इसका कर्ण है, जैसा कि हम निश्चित रूप से जानते हैं। रहने वाले पक्ष को विपरीत के रूप में जाना जाता है। इस तरह, संख्यात्मक रूप से, हम पाइथागोरस प्रमेय के रूप में बोलते हैं:)
Hypotenuse2 = Perpendicular2 + Base2
Pythagorean Theorem Derivation :-
Consider a right-angled triangle ΔABC. From the beneath figure, it is right-angled at B.
Pythagoras Theorem Derivation - 1
Leave BD alone opposite to the side AC.
Pythagoras Theorem Derivation - 2
From the above-given figure, think about the ΔABC and ΔADB,
In ΔABC and ΔADB
∠ABC =∠ADB=90°
∠A = ∠A → normal
Utilizing the AA rule for the likeness of triangles,
ΔABC ≅ ΔADB
Along these lines, AD/AB = AB/AC
⇒ AB2 = AC x AD … (1)
Considering ΔABC and ΔBDC from the beneath figure.
Pythagoras Theorem Derivation - 3
∠C = ∠C → normal
∠CDB = ∠ABC = 90°
Utilizing the Angle Angle(AA) foundation for the likeness of triangles, we reason that,
ΔBDC ≅ ΔABC
In this manner, CD/BC = BC/AC
⇒ BC2 = AC x CD … ..(2)
From the likeness of triangles, we reason that,
Δ ADB ≅ ∠CDB = 90°
So if an opposite is drawn from the right-angled vertex of a right triangle to the hypotenuse, at that point the triangles framed on the two sides of the opposite are like each other and furthermore to the entire triangle.
To Prove: AC2 =AB2 +BC2
By adding condition (1) with condition (2), we get:
AB2 + BC2= (AC x AD) + (AC x CD)
AB2 + BC2 = AC (AD+CD) … ..(3)
Since AD+CD = AC, substitute this incentive in condition (3)
AB2 + BC2= (AC)
Presently, it becomes
AB2+ BC2= AC2
Henceforth, Pythagoras theorem is demonstrated.
Use of Pythagoras Theorem in Real Life
Coming up next are the uses of the Pythagoras theorem:
Pythagoras theorem is utilized to check if a given triangle is a right-angled triangle or not.
Aerospace researchers and meteorologists discover the range and sound source utilizing the Pythagoras theorem.
It is utilized by oceanographers to decide the speed of sound in water.
Pythagorean Theorem Examples and Solutions
Question 1: Find the hypotenuse of a triangle whose lengths of different sides are 4 cm and 10cm.
Arrangement: Using the Pythagoras theorem,
Hypotenuse2=Perpendicular2+Base2
Hypotenuse2=102+42
Hypotenuse=102+42‾‾‾‾‾‾‾‾√=116‾‾‾‾√=10.77cm
Subsequently the hypotenuse of the triangle is 10.77 cm.
Question 2: If the hypotenuse of a right-angled triangle is 13 cm and one of the different sides is 5 cm, locate the third side.
Arrangement: Given,
Hypotenuse a= 13 cm
One side b = 5 cm
Another side c=?
Utilizing the Pythagoras theorem,
a2=b2+c2
132=52+C2
C2=132−52‾‾‾‾‾‾‾‾√=169−25‾‾‾‾‾‾‾‾‾√=144‾‾‾‾√=12cm
Subsequently the hypotenuse of the triangle is 12cm.
To tackle more issues on the point, download Byju's - The Learning App.
Every now and again Asked Questions on Pythagorean Theorem Formula
What is the recipe for Pythagoras Theorem?
The equation for Pythagoras Theorem is given by:
Hypotenuse^2 = Perpendicular^2 + Base^2
Or on the other hand
c^2 = a^2+b^2
Where a,b and c are the sides of the right-angled triangle.
What is implied by Pythagoras Theorem?
The Pythagoras theorem expresses that the square of the length of the hypotenuse is equivalent to the aggregate of squares of the lengths of other different sides of the right-angled triangle.
What is the utilization of Pythagoras Theorem?
The Pythagoras theorem otherwise called Pythagorean theorem is utilized to discover the sides of a right angled triangle. This theorem is for the most part utilized in Trigonometry, where we utilize trigonometric proportions, for example, sine, cos, tan to discover the length of the sides of the right triangle.
What is the genuine utilization of Pythagoras Theorem Formula?
The length of inclining associating two structures can be determined utilizing this recipe.
Likewise, we utilize this equation alongside trigonometry idea, to discover angle of rise if an individual seeing an article kept at top of the structure as for level line. Angle of sadness is determined when the article is kept underneath the view of the individual.
Hypotenuse2 = Perpendicular2 + Base2
Pythagorean Theorem is one of the most principal theorems in science and it characterizes the connection between the three sides of a right-angled triangle. You are now mindful of the definition and properties of a right-angled triangle. It is the triangle with one of its angles as a right angle, that is, 90 degrees. The side that is inverse to the 90-degree angle is known as the hypotenuse. The other different sides that are adjacent to the right angle are called legs of the triangle.
(पायथागॉरियन प्रमेय विज्ञान में सबसे प्रमुख प्रमेयों में से एक है और यह एक समकोण त्रिभुज के तीन पक्षों के बीच संबंध की विशेषता है। अब आप एक समकोण त्रिभुज की परिभाषा और गुणों से सावधान हैं। यह एक समकोण के रूप में एक कोण है, जो कि 90 डिग्री है। वह पक्ष जो 90 डिग्री के कोण पर उलटा होता है, कर्ण के रूप में जाना जाता है। दूसरे अलग-अलग पक्ष जो समकोण के समीप होते हैं, उन्हें त्रिभुज के पैर कहा जाता है।)
The Pythagoras theorem, otherwise called the Pythagorean theorem, expresses that the square of the length of the hypotenuse is equivalent to the total of squares of the lengths of other different sides of the right-angled triangle. Or on the other hand, the aggregate of the squares of the two legs of a right triangle is equivalent to the square of its hypotenuse.
(पाइथागोरस प्रमेय, जिसे अन्यथा पाइथागोरस प्रमेय कहा जाता है, व्यक्त करता है कि कर्ण की लंबाई का वर्ग समकोण त्रिभुज के अन्य विभिन्न पक्षों की लंबाई के वर्गों के कुल के बराबर है। या दूसरी ओर, एक दाहिने त्रिभुज के दो पैरों के वर्गों का कुल इसके कर्ण के वर्ग के बराबर है।)
Pythagoras Theorem FormulaLet us consider one of the legs on which the triangle rests as its base. The side inverse to the right angle is its hypotenuse, as we definitely know. The staying side is known as the opposite. In this way, numerically, we speak to the Pythagoras theorem as:
(पाइथागोरस प्रमेय सूत्र हमें उन पैरों में से एक मानते हैं जिन पर त्रिकोण अपना आधार बनाता है। दाहिने कोण पर उलटा इसका कर्ण है, जैसा कि हम निश्चित रूप से जानते हैं। रहने वाले पक्ष को विपरीत के रूप में जाना जाता है। इस तरह, संख्यात्मक रूप से, हम पाइथागोरस प्रमेय के रूप में बोलते हैं:)
Hypotenuse2 = Perpendicular2 + Base2
Pythagorean Theorem Derivation :-
Consider a right-angled triangle ΔABC. From the beneath figure, it is right-angled at B.
Pythagoras Theorem Derivation - 1
Leave BD alone opposite to the side AC.
Pythagoras Theorem Derivation - 2
From the above-given figure, think about the ΔABC and ΔADB,
In ΔABC and ΔADB
∠ABC =∠ADB=90°
∠A = ∠A → normal
Utilizing the AA rule for the likeness of triangles,
ΔABC ≅ ΔADB
Along these lines, AD/AB = AB/AC
⇒ AB2 = AC x AD … (1)
Considering ΔABC and ΔBDC from the beneath figure.
Pythagoras Theorem Derivation - 3
∠C = ∠C → normal
∠CDB = ∠ABC = 90°
Utilizing the Angle Angle(AA) foundation for the likeness of triangles, we reason that,
ΔBDC ≅ ΔABC
In this manner, CD/BC = BC/AC
⇒ BC2 = AC x CD … ..(2)
From the likeness of triangles, we reason that,
Δ ADB ≅ ∠CDB = 90°
So if an opposite is drawn from the right-angled vertex of a right triangle to the hypotenuse, at that point the triangles framed on the two sides of the opposite are like each other and furthermore to the entire triangle.
To Prove: AC2 =AB2 +BC2
By adding condition (1) with condition (2), we get:
AB2 + BC2= (AC x AD) + (AC x CD)
AB2 + BC2 = AC (AD+CD) … ..(3)
Since AD+CD = AC, substitute this incentive in condition (3)
AB2 + BC2= (AC)
Presently, it becomes
AB2+ BC2= AC2
Henceforth, Pythagoras theorem is demonstrated.
Use of Pythagoras Theorem in Real Life
Coming up next are the uses of the Pythagoras theorem:
Pythagoras theorem is utilized to check if a given triangle is a right-angled triangle or not.
Aerospace researchers and meteorologists discover the range and sound source utilizing the Pythagoras theorem.
It is utilized by oceanographers to decide the speed of sound in water.
Pythagorean Theorem Examples and Solutions
Question 1: Find the hypotenuse of a triangle whose lengths of different sides are 4 cm and 10cm.
Arrangement: Using the Pythagoras theorem,
Hypotenuse2=Perpendicular2+Base2
Hypotenuse2=102+42
Hypotenuse=102+42‾‾‾‾‾‾‾‾√=116‾‾‾‾√=10.77cm
Subsequently the hypotenuse of the triangle is 10.77 cm.
Question 2: If the hypotenuse of a right-angled triangle is 13 cm and one of the different sides is 5 cm, locate the third side.
Arrangement: Given,
Hypotenuse a= 13 cm
One side b = 5 cm
Another side c=?
Utilizing the Pythagoras theorem,
a2=b2+c2
132=52+C2
C2=132−52‾‾‾‾‾‾‾‾√=169−25‾‾‾‾‾‾‾‾‾√=144‾‾‾‾√=12cm
Subsequently the hypotenuse of the triangle is 12cm.
To tackle more issues on the point, download Byju's - The Learning App.
Every now and again Asked Questions on Pythagorean Theorem Formula
What is the recipe for Pythagoras Theorem?
The equation for Pythagoras Theorem is given by:
Hypotenuse^2 = Perpendicular^2 + Base^2
Or on the other hand
c^2 = a^2+b^2
Where a,b and c are the sides of the right-angled triangle.
What is implied by Pythagoras Theorem?
The Pythagoras theorem expresses that the square of the length of the hypotenuse is equivalent to the aggregate of squares of the lengths of other different sides of the right-angled triangle.
What is the utilization of Pythagoras Theorem?
The Pythagoras theorem otherwise called Pythagorean theorem is utilized to discover the sides of a right angled triangle. This theorem is for the most part utilized in Trigonometry, where we utilize trigonometric proportions, for example, sine, cos, tan to discover the length of the sides of the right triangle.
What is the genuine utilization of Pythagoras Theorem Formula?
The length of inclining associating two structures can be determined utilizing this recipe.
Likewise, we utilize this equation alongside trigonometry idea, to discover angle of rise if an individual seeing an article kept at top of the structure as for level line. Angle of sadness is determined when the article is kept underneath the view of the individual.
Hypotenuse2 = Perpendicular2 + Base2
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