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Solution


Q.

A clinometer is used to determine the height of a vertical cliff (an instrument used for measuring the angle or elevation of slopes). The angle of elevation is measured from 2 points (A and B respectively), which are 100 m and 200 m away from the base of the cliff.
At A and B, which of the following scenarios are possible

(i) The angles of elevation from A and B to the top of the cliff are the same.
(ii) The angle of elevation from A is greater than the angle of elevation at B.
(iii) The angle of elevation at A is twice the angle of elevation at B.
(iv) B is farther from the cliff than A
1 (ii) only  
2 (ii) and (iv) only  
3 (i) and (iii) only
 
4 (ii), (iii) and (iv) only  

Ans.

(2)

(i) Cannot be true (as angle of elevation will differ by the distance of the point to the base of the cliff).

(ii) If the angle of elevation at A is greater than at B, it indicates that A is closer to the cliff (which is suggested by the data).

(iii) Let CD be the vertical cliff.Then,∠CAD=θ and∠CBD=ϕ.In∆ACD,we have: tanθ=CDAC⇒tanθ=h100…iIn∆BCD,we have:tanϕ=CDBC⇒tanϕ=h200…iiFrom (i) and (ii):tanθ=2tanϕSo,θ≠2ϕ.Thus, statement (iii) is not possible.

(iv) B is farther (as suggested by the data).