Questions in trigonometry

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An aeroplane flying horizontally 1 km above the ground is observed at an elevation of 60° and after 10 seconds the elevation is observed to be 30°. The uniform speed of the aeroplane in $km/h$ is
From a point a metre above a lake the angle of elevation of a cloud is $\alpha$ and the angle of depression of its reflection is $\beta$. The height of the cloud is
If the angle of depression of a point A on the ground from the top of a tower be 30°, then the angle of elevation of the top of the tower from the point A will be
Two vertical poles of equal heights are 120 m apart. On the line joining their bottoms, A and B are two points. Angle of elevation of the top of one pole from A is 45° and that of the other pole from B is also 45°. If AB = 30 m, then the height of each pole is
At a distance 2h from the foot of a tower of height h, the tower and a pole at the top of the tower subtend equal angles. Height of the pole should be
A house subtends a right angle at the window of an opposite house and the angle of elevation of the window from the bottom of the first house is 60°. If the distance between the two houses be 6 metres, then the height of the first house is
The angle of elevation of the sun, when the shadow of the pole is $\sqrt{3}$ times the height of the pole, is
A ladder rests against a wall so that its top touches the roof of the house. If the ladder makes an angle of 60° with the horizontal and height of the house be $6\sqrt{3}$ meters, then the length of the ladder is
If the angles of elevation of two towers from the middle point of the line joining their feet be 60° and 30° respectively, then the ratio of their heights is
At a point on the ground the angle of elevation of a tower is such that its cotangent is 3/5. On walking 32 metres towards the tower the cotangent of the angle of elevation is 2/5. The height of the tower is

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