Q19 of 35 Page 219

A bridge across a valley is h metres long. There is a temple in the valley directly below the bridge. The angles of depression of the top of the temple from the two ends of the bridge have measures α and β. Prove that the height of the bridge above the top of the temple is

Let AD be the bridge and E be the top of the temple.



The perpendicular from E on AD is EF.


Thus, EF represents the height from the top of the temple to the bridge.


Let EF = x and DF = y


AF = h – y


In ∆ABE,




………(1)


In ∆DCE,



………..(2)


From (1) and (2),



h tan α tan ß – x tan ß = x tan α


h tan α tan ß = x(tan α + tan ß)



The height of the bridge above the top of the temple is .


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If the angle of elevation of a cloud from a point h metres above a lake has measure a and the angle of depression of its reflection in the lake has measure β, prove that the height of the h(tani3 + tana) cloud is .

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From the top of a building , 60 m high, the angles of depression of the top and bottom at a vertical lamp post are observed to have measure 30 and 60 respectively. Find,

(1) the horizontal distance between building and lamp post.


(2) the height of the lamp post.


(3) the difference between the heights of the building and the lamp post.

 20

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is . On walking 192 metres towards the tower, the tangent of the angle is found to be. Find the height of the tower.

 21

A statue 1.46 m tall, stands on the top of a pedestal. From the point on the ground the angle of elevation of the top of the statue has measure 60 and from the same point, the angle of elevation of the top of the pedestal has measure 45. Find the height of the pedestal.