The lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed to be 60o and 30o, respectively. Find the height of the balloon above the ground.
A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite side of the lane are found to be α and β, respectively. Prove that the height of the other house is h ( 1 + tan α cot β ) metres.
The angle of elevation of the top of a vertical tower from a point on the ground is 60o . From another point 10 m vertically above the first, its angle of elevation is 45o. Find the height of the tower.
From the top of a tower h m high, the angles of depression of two objects, which are in line with the foot of the tower are α and β (β > α). Find the distance between the two objects.
The angle of elevation of the top of a tower 30 m high from the foot of another tower in the same plane is 60° and the angle of elevation of the top of the second tower from the foot of the first tower is 30°. Find the distance between the two towers and also the height of the other tower.
If sinθ + cosθ = p and secθ + cosecθ = q, then prove that q (p2 – 1) = 2p.
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower.
Given that sinθ + 2cosθ = 1, then prove that 2sinθ – cosθ = 2.
If 1 + sin2θ = 3sinθ cosθ , then prove that tanθ = 1 or 1/2
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