Grade 12Algebra

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 ?

sudhanshu

12 Years agoGrade 12

2 Answers

SHAIK AASIF AHAMED

12 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

6 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