Q54 of 107 Page 12

A ladder rests against a wall at an angle α to the horizontal. Its foot is pulled away from the wall through a distance a, so that it slides a distance b down the wall making an angle β with the horizontal. Show that

In the fig let the length of ladder is h (m)


In ∆AEB


Sin α =


Sin α =


AE = h Sin α


Cos α =


Cos α =


BE = h Cos α


In ∆DEC


Sin β =



Sin β =


DE = h Sin β


Cos β =


Cos β =


CE = h Cos β


Now


=


=


=


= Proved


More from this chapter

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52

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive mile stones on opposite sides of the aeroplane are observed to be α and β. Show that the height in miles of aeroplane above the road is given by

53

PQ is a post of given height a, and AB is a tower at some distance. If α and β are the angles of elevation of B, the top of the tower, at P and Q respectively. Find the height of the tower and its distance from the post.

 55

A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b metres just above A is β. Prove that the height of the tower is b tan α cot β.

 56

An observer, 1.5 m tall, is 28.5 m away from a tower 30 m high. Determine the angle of elevation of the tower from his eye.