Q100 / 160 · WBJEE 2011 · Mathematics

If in a triangle \(A B C, \sin A, \sin B, \sin C\) are in A.P., then

A
the altitudes are in A.P.
Correct answer
B
the altitudes are in H.P.
C
the angles are in A.P.
D
the angles are in H.P.

Solution

Hints: \(\frac{1}{2} \mathrm{ap}_1=\frac{1}{2} \mathrm{bp}_2=\frac{1}{2} \mathrm{cp}_3=\Delta\) \(\mathrm{a}=\frac{2 \Delta}{\mathrm{p}_1}\left|\mathrm{~b}=\frac{2 \Delta}{\mathrm{p}_2}\right| \mathrm{c}=\frac{2 \Delta}{\mathrm{p} 3}\) H.P.

Hence, the correct answer is option: 'B'.

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