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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 & Solution
Correct Answer:
Option
C

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