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At a point on a horizontal line through the base of a monument the angle of elevation of the top of the monument is found to be such that its tangent is \( \Large \frac{1}{5} \) On walking 138 metres towards the monument the secant of the angle of elevation is found to be \( \Large \frac{\sqrt{193}}{12} \). The height of the monument (in metre) is

A) 42
B) 49
C) 35
D) 56

Correct Answer:

A) 42

Description for Correct answer:

\( \Large \textbf{Shortcut approach} \)

\( \Large \textbf{Ist Case:} \)

\( \Large tan \theta =\frac{AB}{BC}=\frac{Perpendicular}{Base}=\frac{1}{5} \)

\( \Large \textbf{IInd Case:} \)

\( \Large Sec \alpha =\frac{AD}{BD}=\frac{Hypo}{Base} \)

\( \Large \frac{\sqrt{193}}{12} \)

\( \Large In\ \triangle ABD \)

\( \Large Hypo=\sqrt{193} \)

\( \Large Base=12 \)

Then perpendicular = 7

(By pythagoras theorem)

In both case perpendicular will be equal

\( \Large tan \theta =\frac{1 \times 7}{5 \times 7}=\frac{7\leftarrow Perpen}{35\leftarrow Base} \)

\( \Large AB = 42 m \)

Part of solved Height and Distance questions and answers : >> Elementary Mathematics >> Height and Distance

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