question_answer

A player sitting on the top of a tower of height 40 m observes the angle of depression of a bail lying on the ground is \[{{60}^{o}}\]. The distance between the foot of the tower and the ball is

A)  \[\frac{50}{\sqrt{3}}m\]                   

B)  \[\frac{40}{\sqrt{3}}m\]       

C)         \[40\sqrt{3}\,m\]        

D)         \[50\sqrt{3}\,m\]        

Correct Answer: B

Solution :

Height of tower = 40 m Angle of depression \[={{60}^{o}}\]                         \[\Rightarrow \] \[\angle CAB={{90}^{o}}-{{60}^{o}}={{30}^{o}}\] In \[\Delta \,ABC,\frac{BC}{AB}=\tan {{30}^{o}}\] \[\Rightarrow \] \[\frac{BC}{40}=\frac{1}{\sqrt{3}}\Rightarrow BC=\frac{40}{\sqrt{3}}m\] Hence, the distance between the foot of the tower and ball \[\frac{40}{\sqrt{3}}m.\]