question_answer

 If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of \[2\sqrt{3}\,metres\] along the ground, then the angle (in degrees) that the sun makes with the ground is  [EAMCET 1990]

A) \[{{60}^{o}}\]

B) \[{{80}^{o}}\]

C) \[{{75}^{o}}\]

D) None of these

Correct Answer: A

Solution :

Accordingly,  \[\tan \theta =\frac{h}{x}=\frac{h+6}{x+2\sqrt{3}}=\frac{6}{2\sqrt{3}}\Rightarrow \theta ={{60}^{o}}\][Since the triangles \[60-x=\sqrt{3}(\sqrt{3}x)\] and \[\frac{60}{4}=x\Rightarrow x=15\] are similar].