Question

from a top of a hill, the angle of depression of two consecutive kilometre stones , due east , are found to be 30^ and 45^ respectively. Find the distance of two stones from the foot of the hill

Answer 1

Let the height of the hill AB = h km

C and D are two stones of the hill at a distance of 1 km .

Angles of depression of C and D 45° and 30° respectively.

Assume that Distance from foot of the hill to first stone AC = x km.

Then Distance between two stones = x + 1 km

In a traingle CAB,

tan 45° = AB / AC

1 = h / x

h = x  --------(1)

In a traingle DAB,

tan 30° = AB / AD

⇒ 1 / √3 = h / ( x +1)

⇒ √3 h = ( x + 1)

⇒ √3h = h + 1   ( from (1))

⇒ (√3 - 1) h = 1

⇒ h = 1 / (√3 - 1)    (rationalize denominator )

⇒ h = (√3 + 1) / 2 = ( 1.732 +1) / 2

∴ h = 2.732 / 2 = 1.366.

∴ x = 1.366.

∴ distance of the two stones from the foot of the hill = x + 1 = 1.366 + 1 = 2.366

Answer 2

Answer:

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