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Question

If θ1 and θ2 be the apparent angles of dip observed in two vertical planes at right angles to each other, then the true angle of dip θ is given

A
tan2θ=tan2θ1tan2θ2
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B
cot2θ=cot2θ1+cot2θ2
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C
tan2θ=tan2θ1+tan2θ2
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D
cot2θ=cot2θ1cot2θ2
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Solution

The correct option is B cot2θ=cot2θ1+cot2θ2
angle of dip, tanθ=verticalHorizontal=vH
Case 1: tanθ1=vH1
Case 2: tanθ2=vH2
As given, H1 and H2 are
Then, H2=H21+H22(1)
putting above values in eq. (1)
we get,
(vtanθ)2=(vtanθ1)2+(vtanθ2)2

cot2θ=cot2θ1+cot2θ2

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