Questions in trigonometry

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A balloon is observed simultaneously from three points A, B and C on a straight road directly under it. The angular elevation at B is twice and at C is thrice that of A. If the distance between A and B is 200 metres and the distance between B and C is 100 metres, then the height of balloon is given by
A vertical pole (more than 100 m high) consists of two portions, the lower being one-third of the whole. If the upper portion subtends an angle ${{\tan }^{-1}}\frac{1}{2}$ at a point in a horizontal plane through the foot of the pole and distance 40 ft from it, then the height of the pole is
A flag-post 20m high standing on the top of a house subtends an angle whose tangent is $\frac{1}{6}$ at a distance 70 m from the foot of the house. The height of the house is
A balloon is coming down at the rate of 4 m/min. and its angle of elevation is 45° from a point on the ground which has been reduced to 30° after 10 minutes. Balloon will be on the ground at a distance of how many meters from the observer
A person standing on the bank of a river finds that the angle of elevation of the top of a tower on the opposite bank is 45°. Then which of the following statements is correct
AB is a vertical pole resting at the end A on the level ground. P is a point on the level ground such that AP = 3 AB. If C is the mid-point of AB and CB subtends an angle $\beta$ at P, the value of $\tan \beta $ is
Two straight roads intersect at an angle of 60°. A bus on one road is 2 km away from the intersection and a car on the other road is 3 km away from the intersection. Then the direct distance between the two vehicles is
If a flagstaff of 6 metres high placed on the top of a tower throws a shadow of $2\sqrt{3}\,metres$ along the ground, then the angle (in degrees) that the sun makes with the ground is
The angle of elevation of a cliff at a point A on the ground and a point B, 100 m vertically at A are $\alpha$ and $\beta$ respectively. The height of the cliff is
A flag-staff of 5 m high stands on a building of 25 m high. At an observer at a height of 30 m. The flag-staff and the building subtend equal angles. The distance of the observer from the top of the flag-staff is

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