91Ó°ÊÓ

On level ground the angle of elevation of the top of the tower is \(30^{\circ} .\) On moving 20 meters near then the angle of elevation is \(60^{\circ} .\) The height of the tower is (a) \(20 \sqrt{3} \mathrm{~m}\) (b) \(10 \sqrt{3} \mathrm{~m}\) (c) \(10(\sqrt{3}-1) m\) (d) None

From the top of a light house 60 meters high with its base at sea level, the angle of depression is \(15^{\circ}\). The distance of the boat from the foot of the light house is (a) \(60 \times\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right) m\) (b) \(60 \times\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right) m\) (c) \(\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right) m\) (d) None

From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive milestones on opposite sides of the aeroplane are observed to \(45^{\circ}\) and \(60^{\circ}\). Then the height in miles of aeroplane above the road is (a) \(\frac{\sqrt{3}}{\sqrt{3}+1}\) (b) \(\frac{\sqrt{3}}{\sqrt{3}-1}\)

A vertical tower erected at the focus of the parabola \(y^{2}=40 x\) subtends an angle \(\frac{\pi}{3}\) at the vertex of the parabola. If the tower subtends an angle \(\frac{\pi}{6}\) at a point \(P\) lying on the parabola. Then find the possible co-ordinates of point \(P\).(c) \(\frac{\sqrt{3}+1}{\sqrt{3}-1}\) (d) \(\frac{\sqrt{3}-1}{\sqrt{3}+1}\)