In Delta PQR,if sin P, sin Q and sin R are in | vedclass

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(B) Let $h_1, h_2, h_3$ be the altitudes of $	riangle PQR$ corresponding to sides $a, b, c$ respectively.Area of $	riangle PQR = \frac{1}{2} 	imes

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its altitudes are in $H$.$P$.

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(B) Let $h_1, h_2, h_3$ be the altitudes of $	riangle PQR$ corresponding to sides $a, b, c$ respectively.Area of $	riangle PQR = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.$	ext{Area} = \frac{1}{2} a h_1 = \frac{1}{2} b h_2 = \frac{1}{2} c h_3$.Thus,$h_1 = \frac{2 	imes 	ext{Area}}{a}$,$h_2 = \frac{2 	imes 	ext{Area}}{b}$,and $h_3 = \frac{2 	imes 	ext{Area}}{c}$.By the sine rule,$\frac{a}{\sin P} = \frac{b}{\sin Q} = \frac{c}{\sin R} = 2R$ (where $R$ is the circumradius).So,$a = 2R \sin P$,$b = 2R \sin Q$,and $c = 2R \sin R$.Since $\sin P, \sin Q, \sin R$ are in $A$.$P$.,it follows that $a, b, c$ are in $A$.$P$.Therefore,$\frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in $H$.$P$.Substituting $a, b, c$ in terms of $h_1, h_2, h_3$,we get $\frac{h_1}{2 	imes 	ext{Area}}, \frac{h_2}{2 	imes 	ext{Area}}, \frac{h_3}{2 	imes 	ext{Area}}$ are in $H$.$P$.Hence,the altitudes $h_1, h_2, h_3$ are in $H$.$P$.

In $\Delta PQR$,if $\sin P, \sin Q$ and $\sin R$ are in $A$.$P$.,then:

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