A and B are 2 points on level ground, and B is a metres due east of A; a tower, h metres high , is also on the same level ground. From A the tower is in a direction of N θ E and from B it is N $\phi$ W. From the top of the tower, the angle of depression of A is α and of B it is β. Prove:
$(i) h\sin(\theta + \phi) = a\cos\phi\ \tan\alpha \\(ii) cos\phi \tan\alpha = cos\theta\tan\beta \\(iii)h^2(\cot^2\alpha - \cot^2\beta) - 2ha\cot\alpha\sin\theta + a^2 = 0$
I think the question may be wrong. I do not find either (i) or (ii) true so haven’t proceeded to (iii). I should be grateful if anyone could confirm or refute i or ii.