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From a window {h meters above the ground} of a house in a street the angles of elevation and depression of the top and the foot of another house of opposite side of the street are 'a' and 'b' respectively. Show that the opposite height of house is h(1 + tan a cot b).
tanb= h/x x= h/tanb = hcotb----- 1 tana= y/x y= x*tana -----2 substituting for x y= h*cotb*tana therefore total height of the building = h+y h+y = h + h*cotb*tana h +y = h( 1+cotb*tana) hence proved
tanb= h/x
x= h/tanb = hcotb----- 1
tana= y/x
y= x*tana -----2
substituting for x
y= h*cotb*tana
therefore total height of the building = h+y
h+y = h + h*cotb*tana
h +y = h( 1+cotb*tana)
hence proved
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