Question
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The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b
What is MN equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
\( \tan(60^\circ) = \frac{h}{x} \Rightarrow h = \sqrt{3}x \)
\( \tan(45^\circ) = \frac{h}{b + x} \Rightarrow h = b + x \)
\( h = b + x \Rightarrow \sqrt{3}x = b + x \)
\( x = \frac{b(\sqrt{3} + 1)}{2} \)
\( h = MN = \sqrt{3}x = \left( \frac{3 + \sqrt{3}}{2} \right) b \)
Hence, the correct answer is Option 1.
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