From the bottom of a pole of height h, the angle of elevation of the top of a tower is `alpha`. The pole subtends an angle `beta` at the top of the tower. find the height of the tower.
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1)`tanalpha=4/x`
`90-(90-alpha+beta)`
`90-90+alpha-beta`
2)`tan(alpha-beta)=(4-h)/x`
`tan(apha-beta)=(H-h)/(H/tanalpha)`
`tan(alpha-beta)=(H-h)/Htanalpha`
`h/H=1-tan(alpha-beta)/tanalpha`
`h/H=(tanalpha-tan(alpha-beta))/tanalpha`
`h/H=1-tan(alpha-beta)/tanalpha`
`=1-sin(alpha-beta)/cos(alpha-beta)*cosalpha/sinalpha`
`h/H=(sinalphacos(alpha-beta)-sin(alpha-beta)cosalpha)/(sinalphacos(alpha-beta)`
`h/H=sinn(alpha-alpha+beta)/sinalphacos(alpha-beta)`
`H=(hsinalphacos(alpha-beta))/sinbeta`.