Two posts are k metres apart and the height of one is double that of the other. If from the middle point of the line joining their feet, an observer finds the angular elevations of their tops to be complementary, then find the height (in metres) of the shorter post.
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let the height of the smaller pole be h
therefore height of larger one = 2h
let angle of elevation to smaller pole be α
therefore angle of elevation to larger one = (90 - α)
therefore tan α = h/(k/2) = 2h/k (as the viewer is observing from midpoint of k)
also tan(90 - α) = 2h/(k/2)
⇒cotα = 4h/k
∵ tanα * cotα = 1
∴2h/k * 4h/k = 1
8h² = k²
h² = k²/8
h = k/√2
h = k√2/2
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therefore height of larger one = 2h
let angle of elevation to smaller pole be α
therefore angle of elevation to larger one = (90 - α)
therefore tan α = h/(k/2) = 2h/k (as the viewer is observing from midpoint of k)
also tan(90 - α) = 2h/(k/2)
⇒cotα = 4h/k
∵ tanα * cotα = 1
∴2h/k * 4h/k = 1
8h² = k²
h² = k²/8
h = k/√2
h = k√2/2
pls mark as brainliest
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