IIT-JEE 1998Question 1
If in a triangle $PQR$, $\sin P,\sin Q,\sin R$ are in $A.P.$, then
Trigonometric Ratio & Identities
Solution
Concept. By the sine rule the sides are in A.P.; each altitude is $\frac{2\Delta}{\text{side}}$. Formulas used. (1) $a:b:c=\sin P:\sin Q:\sin R$ and $h_a=\dfrac{2\Delta}{a}$Step 1 - Sides. By (1), $a,b,c$ are in A.P. Step 2 - Altitudes. $\frac{1}{h_a},\frac1{h_b},\frac1{h_c}=\frac{a}{2\Delta},\frac{b}{2\Delta},\frac{c}{2\Delta}$ are in A.P., so the altitudes are in H.P. Answer: (B)