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A flagstaff on the top of tower 80 m hig...

A flagstaff on the top of tower 80 m high, subtends an angle `tan^(-1)(1/9)` at point on the ground 100 m from the tower. The height of flagstaff is

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let height of the flagstaff be x
`tan^-1(1/9) = 2 `
`tan alpha = 1/9`
in ` /_ BCD`
`tan beta = 80/100`
in `/_ ACD`
`tan(alpha + beta) = (80+x)/100`
`(tan alpha + tan beta)/(1- tan alpha* tan beta) = (80 + x)/ 100`
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