A flagpole stands on top of a building. From a point 25 metres away from the base of the building, the angle of elevation to the top of the flagpole is 60°, and to the top of the building is 30°. What is the height of the flagpole? (Round your answer off to the nearest metre, and use √3=1.7)
29 m
Let the building height be \(h_1\) and the total height (building + flagpole) be \(h_2\), with the observation point 25 m from the base.
\(h_1 = 25\tan30^\circ = \dfrac{25}{\sqrt3}\) and \(h_2 = 25\tan60^\circ = 25\sqrt3\).
Flagpole height: \(h_2-h_1 = 25\sqrt3-\dfrac{25}{\sqrt3} = 25\left(\sqrt3-\dfrac{1}{\sqrt3}\right) = 25\times\dfrac{2}{\sqrt3} = \dfrac{50}{\sqrt3}\).
Using \(\sqrt3=1.7\): \(\dfrac{50}{1.7} \approx 29.41\), which rounds to 29 m.
Hence, the height of the flagpole is approximately 29 m.
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If x is the distance of P from the bottom of the pillar, then consider the following statements :
1. x can take two values which are in the ratio 1 : 3
2. x can be equal to the height of the flagstaff
Which of the statements given above is/are correct?
What is a possible value of tan θ ?
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