question_answer

The angle of elevation of the top of an incomplete vertical pillar at a horizontal distance of 100 m from its base is \[\text{4}{{\text{5}}^{\text{o}}}\text{.}\] If the angle of elevation of the top of the complete pillar at the same point is to be 60°, then the height of the incomplete pillar is to be increased by:

A)  \[\text{50}\sqrt{3}\,m\]                             

B)  \[100\,m\]        

C)         \[100(\sqrt{3}-1)\,m\] 

D)  \[100(\sqrt{3}+1)\,m\]

Correct Answer: C

Solution :

In \[\Delta ABC,\] \[\tan {{45}^{o}}=\frac{BC}{AB}\] \[\Rightarrow \]               \[BC=100\] In \[\Delta ABD,\] \[\tan {{60}^{o}}=\frac{BD}{AB}\] \[\Rightarrow \]\[\sqrt{3}=\frac{BC+CD}{100}\] \[\Rightarrow \]\[CD=100\sqrt{3}-100\] \[\Rightarrow \]\[CD=100(\sqrt{3}-1)m\]