question_answer

A flagstaff is upon the top of a building. If at a distance of 40 m from the base of building, the angles of elevation of the top of the flagstaff and building' are 60° and 30° respectively, then the height of the flagstaff is

A)  50m                                     

B) 25m

C) 46.19 m               

D) None of these

Correct Answer: C

Solution :

In \[\Delta ABC\], \[\tan {{30}^{o}}\frac{BC}{40}\] \[\Rightarrow \]               \[BC=\frac{40}{\sqrt{3}}\] In \[\Delta DAB,\tan {{60}^{o}}=\frac{BD}{40}\] \[\Rightarrow \]               \[BD=40\sqrt{3}\] \[\Rightarrow \]               \[DC+BC=40\sqrt{3}\] \[\Rightarrow \]               \[DC+\frac{40}{\sqrt{3}}=40\sqrt{3}\]     [from Eq. (i)] \[\Rightarrow \]\[DC=40\left( \sqrt{3}-\frac{1}{\sqrt{3}} \right)=\frac{80}{\sqrt{3}}\]      \[[\because \sqrt{3}=1.73]\] \[\Rightarrow \]               \[DC=46.19m\]