A) \[a\sqrt{3}\]
B) \[\frac{a\sqrt{3}}{\sqrt{3}-1}\]
C) \[\frac{a(3+\sqrt{3})}{2}\]
D) none of these
Correct Answer: C
Solution :
\[{{\tan }^{{{30}^{o}}}}=\frac{AC}{BC}\] \[\frac{1}{\sqrt{3}}=\frac{x}{BC}\Rightarrow BC=\sqrt{3}x\] \[\tan {{45}^{o}}=\frac{x+a}{DE}\Rightarrow DE=x+a\Rightarrow \sqrt{3}x=a+x\] \[(\sqrt{3}-1)x=a\Rightarrow x=\frac{a}{\sqrt{3}-1}\] Height of the tower \[a+x=a+\frac{a}{\sqrt{3}-1}=a\left[ \frac{\sqrt{3}-1+1}{\sqrt{3}-1} \right]\] \[=\frac{a\sqrt{3}}{\sqrt{3}-1}\times \frac{\sqrt{3}\times 1}{\sqrt{3}+1}\] \[=\frac{a(3+\sqrt{3})}{2}\]You need to login to perform this action.
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