Question

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

• A. A.P.
• B. G.P.
• C. H.P.
• D. None

Answer 1

Answer: (A)

A.P.

Answer 2

Area of DABC = $\frac { 1 } { 2 }$ap₁ = $\frac { 1 } { 2 }$bp₂ = $\frac { 1 } { 2 }$cp₃

D = $\frac { 1 } { 2 }$ap₁ = $\frac { 1 } { 2 }$bp₂ = $\frac { 1 } { 2 }$cp₃

̃ p₁ ×, p₂ ×, p₃ ×

p₁×× , p₂ × ×$\frac { 1 } { \sin B }$, p₃ × × $\frac { 1 } { \sin C }$

̃ If p₁, p₂, p₃ are in H.P.

then sin A, sin B, sin C are in A.P.