Class 10 Exam > Class 10 Questions > ABC is an right angle triangle and PRQ is als...
Start Learning for Free
ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q?
Most Upvoted Answer
ABC is an right angle triangle and PRQ is also right angle triangle an...
Proof:
Given: ABC is a right angle triangle with angle C as 90 degrees.
PRQ is also a right angle triangle with angle R as 90 degrees.
Angle B and angle Q are acute angles.
sin B = sin Q.
To prove: angle B = angle Q.
Proof by contradiction:
Assume that angle B is not equal to angle Q.
Case 1: angle B > angle Q
Let's assume angle B is greater than angle Q.
Since ABC is a right angle triangle, the sum of all angles in a triangle is 180 degrees. Therefore, angle B + angle C + angle A = 180 degrees.
In triangle ABC, angle C = 90 degrees. Substituting the value of angle C, we get angle B + 90 degrees + angle A = 180 degrees.
Simplifying the equation, we have angle B + angle A = 90 degrees.
In triangle PRQ, angle R = 90 degrees. Therefore, angle Q + 90 degrees + angle P = 180 degrees.
Simplifying the equation, we have angle Q + angle P = 90 degrees.
Given that sin B = sin Q, we can write the equation as sin B = sin (90 - angle P).
Using the identity sin (90 - x) = cos x, we have sin B = cos angle P.
Since angle B > angle Q, sin B > sin Q. But from our assumption, sin B = sin Q.
This is a contradiction, as sin B cannot be greater than sin Q when angle B > angle Q.
Therefore, our assumption that angle B > angle Q is false.
Case 2: angle B < angle="" />
Let's assume angle B is less than angle Q.
Using similar logic as in Case 1, we can arrive at a contradiction.
Therefore, our assumption that angle B < angle="" q="" is="" />
Conclusion:
Since both assumptions, angle B > angle Q and angle B < angle="" q,="" lead="" to="" contradictions,="" we="" can="" conclude="" that="" angle="" b="" must="" be="" equal="" to="" angle="" />
Hence, angle B = angle Q.
This proves that if sin B = sin Q, then angle B = angle Q.
Given: ABC is a right angle triangle with angle C as 90 degrees.
PRQ is also a right angle triangle with angle R as 90 degrees.
Angle B and angle Q are acute angles.
sin B = sin Q.
To prove: angle B = angle Q.
Proof by contradiction:
Assume that angle B is not equal to angle Q.
Case 1: angle B > angle Q
Let's assume angle B is greater than angle Q.
Since ABC is a right angle triangle, the sum of all angles in a triangle is 180 degrees. Therefore, angle B + angle C + angle A = 180 degrees.
In triangle ABC, angle C = 90 degrees. Substituting the value of angle C, we get angle B + 90 degrees + angle A = 180 degrees.
Simplifying the equation, we have angle B + angle A = 90 degrees.
In triangle PRQ, angle R = 90 degrees. Therefore, angle Q + 90 degrees + angle P = 180 degrees.
Simplifying the equation, we have angle Q + angle P = 90 degrees.
Given that sin B = sin Q, we can write the equation as sin B = sin (90 - angle P).
Using the identity sin (90 - x) = cos x, we have sin B = cos angle P.
Since angle B > angle Q, sin B > sin Q. But from our assumption, sin B = sin Q.
This is a contradiction, as sin B cannot be greater than sin Q when angle B > angle Q.
Therefore, our assumption that angle B > angle Q is false.
Case 2: angle B < angle="" />
Let's assume angle B is less than angle Q.
Using similar logic as in Case 1, we can arrive at a contradiction.
Therefore, our assumption that angle B < angle="" q="" is="" />
Conclusion:
Since both assumptions, angle B > angle Q and angle B < angle="" q,="" lead="" to="" contradictions,="" we="" can="" conclude="" that="" angle="" b="" must="" be="" equal="" to="" angle="" />
Hence, angle B = angle Q.
This proves that if sin B = sin Q, then angle B = angle Q.
Community Answer
ABC is an right angle triangle and PRQ is also right angle triangle an...
Send me in this only. And with explanation of it .I know whole solution but not get understand let see give in this only my WhatsApp is off yet.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q?
Question Description
ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q?.
ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q?.
Solutions for ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? defined & explained in the simplest way possible. Besides giving the explanation of
ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q?, a detailed solution for ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? has been provided alongside types of ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? theory, EduRev gives you an
ample number of questions to practice ABC is an right angle triangle and PRQ is also right angle triangle and 90 degree angle on C,R. now question starts if angle B and angle Q are acute angle such that sin B= sinQ then prove that angle B= angle Q? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup