Question

Gopi and Gautham stand on opposite sides of a tower. The children and the tower are on a straight line also. Gopi sees the top of the tower at an angle of elevation of ${36}^o$ and Gautham sees it at an angle of elevation of ${52}^o$. The distance between thechildren is 60 metres.
a) Draw a rough figure according to the given information.
b) Find the height of the tower. (Height of children can be neglected. Necessary values can be taken from the following table).

Angle	sin	cos	tan
${36}^o$	0.59	0.81	0.72
${52}^o$	0.79	0.62	1.28

Answer 1

(b) Let AB be the height of the tower.
Let C and D be the point at which Gopi and Gautam are standing respectively.
Let BD = x m
CB = 60-x m
$\tan {36}^o=\frac{AB}{CB}$
$0.72=\frac{AB}{60-x}$
$AB=43.2-0.72x$ ....... (1)
$\tan {52}^o=\frac{AB}{BD}$
$1.28=\frac{AB}{x}$
$AB=1.28x$ ....... (2)
From (1) and (2) we get
$1.28x=43.2-0.72x$
$2x=43.2$
$x=21.6m$
$AB=1.28x=1.28\times 21.6=27.648cm$
Therefore height of the tower is $27.648cm$