# From the top of a hill, the angles of depression of two consecutive km stones due east are found to be 30° and 45°. The height of the hill isA. 1/2(√3 - 1) kmB. 1/2(√3 + 1) kmC. (√3 - 1) kmD. (√3 + 1) km

Let AB be the hill and C, D are the km stones. Join B, C, D. Also join C, D with A. So we get two right-angled triangles ABC and ABD with right angle at B. Draw a line AE parallel to BD. Given that the angles of depression of C and D are 45° and 30° respectively. So, EAD = ADB = 30° and EAC = ACB = 45°. Now, CD = 1km. We are to find the height of the hill, that is, AB.

In ∆ABC,

or,

In ∆ABD,

or,

or,

So, the correct option is (B).

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