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If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in ?

If in a triangle ABC, the altitudes from the vertices A, B, C on opposite sides are in H.P., then sin A, sin B, sin C are in ?

Grade:12

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 years ago
Hello student,
Δ = (1/2)p1a=(1/2)p1b=(1/2)p1c
p1, p2, p3 are in H.P.
⇒ 2Δ/a , 2Δ/b , 2Δ/care in H.P.
⇒ 1/a, 1/b, 1/care in H.P
⇒ a, b, c are in A.P.
⇒ sinA, sinB, sinC are in A.P.
Thanks and Regards
Shaik Aasif
askIITians faculty
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

Δ = (1/2)p1a = (1/2)p1b = (1/2)p1c
p1, p2, p3 are in H.P.
⇒ 2Δ/a , 2Δ/b , 2Δ/c are in H.P.
⇒ 1/a, 1/b, 1/c are in H.P
⇒ a, b, c are in A.P.
⇒ sinA, sinB, sinC are in A.P.

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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