If in a triangle ABC, the altitudes from the vertices A,B,C on opposite sidesare in H.P. then sinA, sinB and sinC are in? (AGP, AP, GP, HP)
by 
Billie
ANSWERS: 1
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If the altitudes are in Harmonic Progression, the bases must be in Arithmetic Progression, since the area is the same each time. And then the sine rule says: a/sinA = b/sinB = c/sinC = 2r so the sins are in HP again. EDIT: Youch that was wrong!! If the altitudes are 1/3, 1/4, 1/5 and the area is 1/2 then the bases are 3,4,5 and we have 3/sin A = 4/sin B = 5/sin C so sin A, sin B, sin C must be in the ratio 3,4,5, in AP. If xy is a constant then x and y are in inverse proportion, but if x/y is a constant then x and y are proportional.
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