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question no 27
let the height of the tower 'AB' be h. P and Q are two points of observation. let BP be a and BQ be b.
/_AQB=© THETA
/_APB=90-©THETA
in rt.∆ABQ,We have
AB/BQ=tan ©
=h/b=tan ©theta...... (1)
& in rt.∆ABP, we have
AB/BP=tan (90-©)
=h/a=cot ©.......(2)
Multiply (1) &(2),we get
tan©×cot©=h/b×h/a
=1=h2/ab[ tan ©×cot©=1][h×h=h square)
=h2=ab
h=√ab
Hence, height of the tower is √ab
let the height of the tower 'AB' be h. P and Q are two points of observation. let BP be a and BQ be b.
/_AQB=© THETA
/_APB=90-©THETA
in rt.∆ABQ,We have
AB/BQ=tan ©
=h/b=tan ©theta...... (1)
& in rt.∆ABP, we have
AB/BP=tan (90-©)
=h/a=cot ©.......(2)
Multiply (1) &(2),we get
tan©×cot©=h/b×h/a
=1=h2/ab[ tan ©×cot©=1][h×h=h square)
=h2=ab
h=√ab
Hence, height of the tower is √ab
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