question_answer

A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m, from a point on the field, the angles of elevation of the bottom and tip of the flag staff are \[30{}^\circ \] and \[45{}^\circ \] respectively. Which one of the following gives the best approximation to the following gives the best approximation to the height of the tower?

A) \[3.90m\]

B) \[4.00m\]

C) \[4.10m\]

D) \[4.25m\]

Correct Answer: C

Solution :

[c] as \[\angle CPA=45{}^\circ \]

so \[AC=AP=x+3\]

\[\tan 30{}^\circ =\frac{AB}{AP}=\frac{x}{x+3}\]

\[\frac{1}{\sqrt{3}}=\frac{x}{x+3}\]

\[x+3=\sqrt{3}x\]

\[x=\frac{3}{\sqrt{3}-1}\times \frac{(\sqrt{3}+1)}{(\sqrt{3}+1)}\]

\[x=\frac{3\times 2.73}{2}=\frac{8.19}{2}=4.095m\approx 4.1m\]