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Question

Let â–³ABC,x,y,z are the length of altitudes drawn from A,B,C respectively.

If x,y,z are in A.P. then?

A
cosA,cosB,cosC are in A.P.
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B
cosA,cosB,cosC are in H.P.
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C
sinA,sinB,sinC are in H.P.
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D
sinA,sinB,sinC are in A.P.
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Solution

The correct option is C sinA,sinB,sinC are in H.P.
It is given that x,y,z are the length of altitudes drawn from A,B,C

Thus the area of the triangle is
Δ=12axx=2Δa=2Δ2RsinA=ΔRsinA

Similarly, y=ΔRsinB,z=ΔRsinC

Given x,y,z are in A.P.
ΔRsinA,ΔRsinB,ΔRsinC are in A.P.

sinA,sinB,sinC are in H.P.

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