question_answer

    A tower subtends an angle of\[30{}^\circ \]at a point on the same level as the foot of the tower and at a second point, h metre above the first, the depression of the foot of the tower is\[60{}^\circ \]. The height of the tower is

A)  \[hm\]                                

B) \[3\,h\,m\]

C)  \[\sqrt{3}\,h\,m\]                          

D)  None of these

Correct Answer: D

Solution :

                Let\[OP=x\]be the height of the tower. In\[\Delta AOP,OA=x\cot 30{}^\circ =x\sqrt{3}\] and in \[\Delta AOB,OA=h\cot 60{}^\circ =\frac{h}{\sqrt{3}}\] \[\therefore \]  \[x=\frac{1}{3}h\]