Question

If in a triangle ABC, sin A, sin B, sin C are in A.P., then –

• A. The altitudes are in A.P.
• B. The altitudes are in H.P.
• C. The altitudes are in G.P.
• D. The medians are in A.P.

Answer 1

Answer: (B)

The altitudes are in H.P.

Answer 2

Let altitudes O from A, B, C be p, q, r, respectively then

p = b sin C

q = c sin A

r = a sin B

∴ p : q : r :: b sin C : c sin A : a sin B

⇒ sin B sin C : sin C sin A : sin A sin B = : $\frac { 1 } { \sin B }$:

$\frac { 1 } { \sin C }$

⇒ ∴ sin A, sin B, sin C are in A.P.

⇒ p, q, r are in H.P.