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Height and Distance is considered one of the most asked concept.
17 Questions around this concept.
A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 450. It flies off horizontally straight away from the point O.After one second, the elevation of the bird from O is reduced to 300. Then the speed (in m/s) of the bird is :
The angle of elevation of the top of a vertical tower from a point A, due east of it is 450. The angle of elevation of the top of the same tower from a point B, due south of A is 300. If the distance between A and B is m , then the height of the tower (in metres), is :
Two ships A and B are sailing straight away from a fixed point O along routes such that AOB is always 1200. At a certain instance, OA = 8 km, OB = 6 km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr) :
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If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the
tower, are 300, 450 and 600 respectively,then the ratio, AB : BC, is :
Height and Distance
Trigonometric ratios are useful to solve problems regarding height and distances around us in real life. It is not possible to measure every distance using measuring tape, for instance, the height of a hill ( distance between its foot and its summit), the altitude of a flying object at a certain time, etc.
Angle of Elevation
The student is looking at the top of the tower. The line AC drawn from the eye of the student to the top of the tower is called the line of sight. The angle BAC, so formed by the line of sight with the horizontal is called the angle of elevation of the top of the tower from the eye of the student. It is called angle of elevation because the object is above the observer’s eye level.
Here α is the angle of elevation.
Angle of Depression
If the object is below the observer’s eye level, the angle between the horizontal line and the line of sight is called the angle of depression of the object.
Here β is the angle of depression.
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