Q. 233.6( 10 Votes )

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 is
A. 1/2(√3 - 1) km

B. 1/2(√3 + 1) km

C. (√3 - 1) km

D. (√3 + 1) km

Answer :

Untitled10.jpg


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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