1.

The shadow of a tower of height (1 +sqrt3 ) metre standing on the ground is found to be 2 metre longer when the sun's elevation is 30^(@), then when the sun's elevation was :

Answer»

`30^(@)`
`45^(@)`
`60^(@)`
`75^(@)`

Solution :Let AB is a TOWER of HEIGHT `(1+sqrt3)` m, BC and BD and BD are its shadows. When the sun's elevation are `30^(@)` and `alpha` (say) respectively and CD = 2M.

`therefore"In triangle ABC,"`
`2+BD=(1+sqrt3)COT 30^(@)`
`or 2+BD=(1+sqrt3)sqrt3`
`or BD=(sqrt3+3)-2=sqrt3+1`
Now, in triangle ABD
`tan alpha=(AB)/(BD)=(1+sqrt3)/(sqrt3+1)=1=1 tan 45^(@)`
`therefore alpha=45^(@)`


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