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?

Answer: Option C

Solution

Answer: Option C

Solution:

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