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In the same situation, a flag is hoisted on top of the building and the angle of elevation of the top of the flagstaff from $P$ becomes $45^{\circ}$. What is the length of the flagstaff? 
A$10(\sqrt{3}-1)\mathrm{m}$
B$10(\sqrt{3}+1)\mathrm{m}$
C$\frac{10}{\sqrt{3}}\mathrm{m}$
D$17.32\mathrm{m}$
Answer & Solution
Correct answer: A. $10(\sqrt{3}-1)\mathrm{m}$
First, from the building alone, $\tan 30^{\circ}=\frac{10}{AP}$ gives $AP=10\sqrt{3}$. If the flagstaff length is $x$, then the total height is $10+x$. Now $\tan 45^{\circ}=\frac{10+x}{10\sqrt{3}}=1$, so $10+x=10\sqrt{3}$ and $x=10(\sqrt{3}-1)\mathrm{m}$.
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