Answer to Question #2654 in Trigonometry for anand
alpha = arctan (L1+L2)/D - arctan L1/D = arctan (L2/D / (1 + L1(L1+L2)/D2)) = arctan (L2D/(D2 +L1(L1+L2)) = arctan(46D/(D2 + 46(46+47)) = arctan(46D/(D2 + 4371))
Let's find the first derivative of this expression and let it to be equal to zero:
arctan(46D/(D2 + 4371))' = - 46(D2- 4371)/(D4+10,858D2 + 19,105,641) = 0
Thus the extrema of this function are D =sqrt(4371) = 66.1 m, D = - sqrt(4371) = -66.1 m (this root doesn't math the conditions or can mean the opposite direction from the statue).
Answer: you should stay 66.11m away from the statue.
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