1.

A vertical pole with height more than 100 m consists of two parts, the lower being one-third of the whole. At a point on a horizontal plane through the foot and 40 m from it,the upper part subtends an angle whose tangent is `1/2` What is the height of the pole

Answer» `tanphi=x/(3*40)`
`tan(theta+phi)=x/40`
`tantheta=1/2`
`(tantheta+tanphi)/(1-tantheta*tanphi)=x/40`
`((1/2)+(x/120))/(1-(1/2*x/120))=x/40`
`(cotx/120)/((240-x)/240)=x/40`
`(2(60+x))/(140-x)=x/40`
`80(60+x)=x(240-x)`
`x^2-160x+4800=0`
`(x-120)(x-40)=0`
`x=40,120`.


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