The respective ratio between the height of tower and the point at some distance from its foot is 57 : 19√3. What is the angle (in degrees) of elevation of the top of the tower?

Solution (By Examveda Team)

$$\eqalign{ & {\text{In }}\Delta ABC \cr & \tan \theta = \frac{{AB}}{{BC}} \cr & \tan \theta = \frac{{57}}{{19\sqrt 3 }} \cr & \tan \theta = \frac{3}{{\sqrt 3 }} \times \frac{{\sqrt 3 }}{{\sqrt 3 }} \cr & \tan \theta = \sqrt 3 \cr & \tan \theta = \tan {60^ \circ } \cr & \therefore \boxed{\theta = {{60}^ \circ }} \cr} $$