question_answer

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

A)  48m                                     

B)  36m

C)  54m                                     

D)  72m

Correct Answer: A

Solution :

In \[\Delta DAB,\,\,\tan \theta =\frac{64}{d}\,\Rightarrow \,d=64\,\cot \,\theta \] In \[\Delta CDE,\,\tan ({{90}^{0}}\,-\theta )\,=\frac{36}{d}\] \[\therefore \,\,\,(1)\times (2)\] \[\Rightarrow \,\,64\times 36\,={{d}^{2}}\] \[\Rightarrow \,d=48\]