question_answer

From a tower of 200 m, the angles of depression of two buildings in opposite sides of the tower are found to be\[\text{6}0{}^\circ \]and\[\text{45}{}^\circ \]. What is the distance between the buildings?

A) 415m                    

B)        315.4m

C) 200 m                   

D)        305 m

Correct Answer: B

Solution :

(b) According to the problem, from the figure, AB is the tower of height 200 m. The distance between the height is \[\text{1}00\text{1}=\text{91}\times \text{1}0+\text{91}\]. \[\text{91}0=\text{91}\times \text{1}0+0\] \[\therefore \] \[=\left( \frac{144}{48}+\frac{384}{48}+\frac{240}{48} \right)=3+8+5=16\] \[\frac{a}{b}\]                           ??(1) \[\frac{c}{d}=\frac{L.C.M.(a,c)}{H.C.F.(b,d)}\] \[\Rightarrow \] \[L.C.M.\]                              ?..(2) \[\frac{6}{14}and\frac{2}{7}\]The required distance \[\Rightarrow \]               \[\frac{L.C.M.(6,2)}{H.C.F.(14,7)}=\frac{6}{7}\] \[\text{7}\times \text{13}+\text{13}=\text{1}0\text{4}=\text{23}\times \text{13}\]