A) \[15\,m,\,\,5\sqrt{3}\,m\]
B) \[15\,m,\,\,6\sqrt{3}\,m\]
C) \[16\,m,\,\,4\sqrt{3}\,m\]
D) \[16\,m,\,\,5\sqrt{3}\,m\]
Correct Answer: A
Solution :
Let AB be the multi storied building of height h and let the distance between two building be x metres. \[\angle XAC=\angle ACB={{60}^{o}}\](Alternate angles) \[\angle XAD=\angle \text{ }ADE={{30}^{o}}\] (Alternate angles) In \[\Delta ADE,\] \[\tan {{30}^{o}}=\frac{AE}{ED}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h-10}{x}\] \[[\,\,\,CB=DE=x]\] \[\Rightarrow \] \[x=\sqrt{3}\,(h-10)\] ?..(1) In \[\Delta \,ACB,\] \[\tan {{60}^{o}}=\frac{h}{x}\Rightarrow \sqrt{3}=\frac{h}{x}\Rightarrow x=\frac{h}{\sqrt{3}}\] ..(2) From (1) and (2), we have \[\sqrt{3}\,(h-10)=\frac{h}{\sqrt{3}}\Rightarrow h=15\,m\] From (2), \[x=\frac{h}{\sqrt{3}}\]So, \[x=\frac{15}{\sqrt{3}}=5\sqrt{3}\,m\] Hence, height of multi storied building = 15 metres Distance between two buildings \[=5\sqrt{3}\] metres.You need to login to perform this action.
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