41.A round balloon of radius r subtends an angle α at the eye of the observer while the angle of elevation of its centre is β. Prove that the height of the centre of the balloon is r sin β . cosec α/2.
3368 Views
Long Answer Type
42.If the angle of elevation of a cloud from a point h metres above a lake is α and the angle of depression of its reflection in the lake be β. Prove that the distance of the cloud from the point of observer is
1314 Views
43.From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by
659 Views
44.From the top of a lighthouse the angle of depression of two ships on the opposite sides of it are observed to be α and β. If the height of the light house be h metres and the line joining the ships passes through the foot of the lighthouse. Show that the distance
between the ship is metres.
2168 Views
Advertisement
45.A ladder rests against a wall at an angle α to the horizontal, its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that .
46.From a window h metres above the ground) of a house in a street, the angles of elevation and depression of the top and the foot of another house on the opposite side of the street are ө and φ respectively. Show that the height of the opposite house is h ( 1 + tan ө. cot φ).
Let C be the position of a window of house AC which is h metres above the ground, i.e., AC = h m. BE be the house on the opposite side of the street. The angle of elevation and depression of the top and foot of the opposite house from the window C be ө and φ respectively.
i.e., ∠DCE = ө and ∠BCD - φ. Let DE = x m In right triangle CDE, we have
In right triangle BCD, we have
Comparing (i) and (ii), we get
Hence, height of the opposite house (BE) = BD + DE = h + x = h + h cot φ . tan ө = h (1 + cot φ . tan ө).
2122 Views
Advertisement
47.From the top of a tower the angles of depression of two objects on the same side of the tower are found to be α and β (α > β). If the distance between the objects is p metres,
show that the height It of the tower is given by h = Also, determine the height of the tower if p = 50 metres, α = 60°, β = 30°.
1906 Views
48.The angle of elevation of a cliff from a fixed point is ө. After going up a distance of K metres towards the top of the cliff at an angle of φ, it is found that the angle of elevation
is α. Show that the height of the cliff is
596 Views
Advertisement
49.Two stations due south of a leaning tower which leans towards the north are at distances a and b from its foot. If, α, β, are the elevations of the top of the tower from these stations,
prove that its inclination ө to the horizontal is given by cot
783 Views
50.A pole 5 m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60° and the angle of depression of the point A from the top of the tower is 45°. Find the height of the tower.