question_answer

From a distance of 100 m from the foot of a building, the angle of elevation of its top is \[\text{3}0{}^\circ \]. What is the height of the building?

A) \[57.7\,m\]

B) \[100\sqrt{3}\,m\]

C) \[5.77\,m\]        

D)        \[\frac{100}{3}\,m\]

Correct Answer: A

Solution :

                               Let AB be the height of the building (x m), BC be the distance of the observer from the foot of the building and the angle of elevation is\[{{6}^{x}}={{(2\times 3)}^{x}}={{2}^{x}}\times {{3}^{x}}\]. Then \[\Rightarrow \] \[{{6}^{x}}\] \[\therefore \] \[{{6}^{x}}\]