From the top of a

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.