question_answer

A house of height 100 m subtends a right angle at the window of an opposite house. If the height of the window is 64 m, then the distance between the two houses is

A) \[48\,m\]

B)                                    \[36\,m\]

C) \[54\,m\]                            

D)    \[72\,m\]

Correct Answer: A

Solution :

                In \[\Delta DAB,\,\,\tan \theta =\frac{64}{d}\Rightarrow d=64\cot \theta \]         ? (1)                 In \[\Delta DCE,\,\,\tan ({{90}^{o}}-\theta )=\frac{36}{d}\]                           ? (2) \[\therefore \,\,(1)\times (2)\] \[\Rightarrow 64\times 36={{d}^{2}}\] \[d=48\]