Answer any One question : The length of the shodow of a post becomes 3 meters smaller when the angle of elevation of the Sun increases from `45^@` to `60^@`. Find the height of the post.

Explanation

Let BD be the shadow of AB when the angle of elevation is `45^(@)` and BC be the length of the shadow of the post AB, when the angle of elevation is `60^(@)`.
Now, from the right-angled triangle ABC er get,
`tan 60^(@) = (AB)/(BC)` [by definition]
or, `sqrt(3)=(AB)/(BC)" "or, " " AB = sqrt(3)BC`
or, `BC= (AB)/(sqrt(3))`.............(1)
Again, from the right-angled triangle ABD we get,
`tan45^(@) = (AB)/(BD)` [ by definition ]
or, `1 = (AB)/(BD) " " or, " " AB = BD " " or, AB = BC + CD`
or, ` AB = (AB)/(sqrt(3))+CD " " or, " " AB - (AB)/(sqrt(3)) = CD " "or, " " AB(1-(1)/(sqrt(3))) = CD`
or, `AB((sqrt(3)-1)/(sqrt(3))) = 3 [ because` CD = 3 metres] or, `AB =(3xxsqrt(3))/(sqrt(3)-1)`
or,` " "AB= (3sqrt(3))/(sqrt(3)-1)xx(sqrt(3)+1)/(sqrt(3)+1) " "or, AB = (3sqrt(3)(sqrt(3)+1))/((sqrt(3))^(2)-(1)^(2))`
or, `AB = (3sqrt(3)(sqrt(3)+1))/(3-1) " "or," "AB= (3sqrt(3)(sqrt(3)+1))/(2)`
or, `" "AB=(9+3sqrt(3))/(2)=(9+3xx1.732)/(2)`
`=(9+5.196)/(2)=(14.196)/(2)`
=7.098