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SUMMARY ANGLE OF ELEVATION The line joining the object and eye of the observer is known as the line of sight and the angle which this line of sight makes with the horizontal drawn through the eye of the observer is known as the angle of elevation. ANGLE OF DEPRESSION When the object is at a lower level than the observer’s eyes, he has to look downwards to have a view of the object. In that case, the angle which the line of sight makes with the horizontal drawn through the observer’s eye is known as the angle of depression. OBJECTIVE 1. The angle of elevation of the top of a tower as observed from a point on the horizontal ground is ‘x’. If we move a distance ’d’ towards the foot of the tower, the angle of elevation increases to ‘y’, then the height of the tower is: 𝑑 tan 𝑥 tan 𝑦 𝑑 tan 𝑥 tan 𝑦 (a) tan 𝑥−tan 𝑦 (b) d(tan 𝑥 + tan 𝑦) (c) d(tan 𝑥 − tan 𝑦) (d) tan 𝑥+tan 𝑦 2.
The angle of elevation of the top of a tower, as seen from two points A and B situated in the same line and at distances ‘p’ and ‘q’ respectively from the foot of the tower, are complementary, then the height of the tower is: 𝑝 (a) Pq (b) 𝑞 (c) √𝑝𝑞 (d) none of these
3.
The angle of elevation of the top of a tower at a distance of height of the tower. 20 (a) 50√3 metres (b) metres (c) – 50 metres √3
4.
50√3 3
metres from the foot is 600. Find the (d) 50 metres
The shadow of a tower, when the angle of the sun is 300, is found to be 5 m longer than when it was 450, then the height of the tower in meters is: 5 5 5 (a) (b) 2 (√3 − 1) (c) 2 (√3 + 1) (d) none of these √3+1
SUBJECTIVE 1. From the top of a light house, the angles 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 ℎ (tan 𝛼+tan 𝛽) passes through the foot of the light house. Show that the distance between the ships is tan 𝛼 tan 𝛽 meters. 2.
A ladder rests against a wall at angle α to the horizontal. Its foot is pulled away from the previous point through a distance ‘a’, so that it slides down a distance ‘b’ on the wall making an angle β with 𝑎 cos 𝛼−cos 𝛽 the horizontal. Show that 𝑏 = sin 𝛽−sin 𝛼 .
3.
From an aero plane vertically above a straight horizontal road, the angle of depression of two consecutive kilometer stones on opposite sides of aeroplane are observed to be α and β. Show that tan 𝛼 tan 𝛽) the height of the aeroplane above the road is tan 𝛼 +tan 𝛽 kilometer. HURRY!! Visit our portal and get your NCERT Solutions UPDATED 2021-22. These all very essential for your exam preparation