A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is 60^ . He moves 60 ~m in the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45^ . Then, the height of the tower (in metres) is

Step-by-step solution

In A B D h=x 3 In B A C aligned B C^2 & =A B^2+A C^2 B C & = x^2+(60)^2 & = x^2+3600 aligned In C B D, 45^ = h 3600+x^2 h= 3600+x^2 h^2-x^2=3600 From Eqs. (i) and (ii), we get gathered 3 x^2-x^2=3600 2 x^2=3600 x^2=1800 gathered From Eqs. (i) and (ii), we get aligned & h^2-1800=3600 & & h^2=5400 & & h=30 6 =30 2 3 & =30 2 3 2 =60 3 2 aligned