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If in a triangle PQR, sin P, sin Q, sin R are in A.P., then
- a)the altitudes are in A.P.
- b)the altitudes are in H.P.
- c)the medians are in G.P.
- d)the medians are in A.P.
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altit...
In ΔPQR let d1, d2, d3 be the altitudes on QR, RP and PQ respectively.
⇒
⇒ d1, d2, d3 are in H.P. (As given that sin P, sin Q, sin R are in A.P.)
Most Upvoted Answer
If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altit...
Explanation:
Altitudes in Harmonic Progression:
- In a triangle, the altitudes are in Harmonic Progression if the sines of the angles are in Arithmetic Progression.
- So, if sin P, sin Q, sin R are in A.P., then the altitudes are in H.P.
Harmonic Progression:
- In mathematics, a harmonic progression is a sequence of numbers in which the reciprocals of the terms are in Arithmetic Progression.
- In a triangle, the lengths of the altitudes are in Harmonic Progression if the sines of the angles are in Arithmetic Progression.
Relation between Sines and Altitudes:
- The lengths of the altitudes in a triangle are inversely proportional to the sines of the corresponding angles.
- This means that if sin P, sin Q, sin R are in A.P., then the reciprocals of the sines (1/sin P, 1/sin Q, 1/sin R) are in A.P.
- Therefore, the lengths of the altitudes are in H.P.
Conclusion:
- In a triangle PQR, if sin P, sin Q, sin R are in A.P., then the altitudes of the triangle are in Harmonic Progression (H.P).
- Hence, option 'B' - the altitudes are in H.P. - is the correct answer.
Altitudes in Harmonic Progression:
- In a triangle, the altitudes are in Harmonic Progression if the sines of the angles are in Arithmetic Progression.
- So, if sin P, sin Q, sin R are in A.P., then the altitudes are in H.P.
Harmonic Progression:
- In mathematics, a harmonic progression is a sequence of numbers in which the reciprocals of the terms are in Arithmetic Progression.
- In a triangle, the lengths of the altitudes are in Harmonic Progression if the sines of the angles are in Arithmetic Progression.
Relation between Sines and Altitudes:
- The lengths of the altitudes in a triangle are inversely proportional to the sines of the corresponding angles.
- This means that if sin P, sin Q, sin R are in A.P., then the reciprocals of the sines (1/sin P, 1/sin Q, 1/sin R) are in A.P.
- Therefore, the lengths of the altitudes are in H.P.
Conclusion:
- In a triangle PQR, if sin P, sin Q, sin R are in A.P., then the altitudes of the triangle are in Harmonic Progression (H.P).
- Hence, option 'B' - the altitudes are in H.P. - is the correct answer.
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If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer?
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If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer?.
If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer?.
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If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer?, a detailed solution for If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of If in a triangle PQR, sin P, sin Q, sin R are in A.P., thena)the altitudes are in A.P.b)the altitudes are in H.P.c)the medians are in G.P.d)the medians are in A.P.Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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