Q. 314.3( 12 Votes )

From the top of a

Answer :

We have


Let height of the hill be h km, which is asked in the question.


Since, the stones are consecutive so CD = 1 km.


In ∆ABD,


[, ]


[, tan 30° = 1/√3]


x + 1 = h√3 …(i)


In ∆ABC,


[, ]


1 = h/x [, tan 45° = 1]


h = x …(ii)


Substituting equation (ii) in equation (i), we get


x + 1 = x√3


x√3 – x = 1


(√3 – 1)x = 1


.


Rationalizing it,


[, (a + b)(a – b) = a2 – b2 and so, (√3 + 1)(√3 – 1) = 3 – 1]


[, √3 = 1.73]


x = 1.365


Thus, height of the hill is 1.365 km.


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