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Q.

The shadow of a tower standing on level ground is found to be 40 m longer when the Sun's altitude is 30 then when it is 60. The height of the tower is ____.

1)h= 203 m
2)h= 103 m
3)h= 53 m
4)h= 303 m

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Detailed Solution

 Question ImageLet the tower be AB
When the Sun's altitude is at 60°
ACB = 60° and the length of the shadow = BC
When the sun's altitude is at 30°
ADB = 30° and the length of the shadow = DB
So the length of the shadow is 40 m when the angle Changes from 60° to 30°
That is CD = 40 m
Now we have to find the height of the tower AB
Here we can see that tower is vertical to ground
So ABC = 90°
So Considering sight-angled triangle ABC,
Question ImageQuestion ImageQuestion ImageQuestion Image   …(1)
Now consider the right- angled triangle ADC.
Question ImageQuestion ImageQuestion ImageQuestion ImageSo we know DC + CB = DB
Question ImageQuestion Image   …(2)
From (1) and (2)
Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageAB = 203 is the height of the tower.
 
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