Question

If in a $△ABC$, the altitudes from the vertices $A,B$ and $C$ on opposite sides are in $H.P.$, then $\sin A,\sin B$ and $\sin C$ are in

• A. G.P.
• B. A.P.
• C. Arithmetic- Geometric Progression
• D. H.P.

Answer 1

The correct option is B A.P.

$△=\frac{1}{2}{P}_{1}a=\frac{1}{2}{P}_{2}b=\frac{1}{2}{P}_{3}c$

$P_1,P_2,P_3$ are in H.P

$⟹\frac{2△}{a},\frac{2△}{b},\frac{2△}{c}$ are in H.P

$⟹\frac{1}{a},\frac{1}{b},\frac{1}{c}$ are in H.P

$⟹a,b,c$ are in A.P

$⟹\sin A,\sin B,\sin C$ are in A.P