Statue

On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.

Correct result:

x =  3.39 m

Solution:

$$\begin{gathered} \alpha (x)=\arctan {\displaystyle \frac{4+2.7-1.7}{x}}-\arctan {\displaystyle \frac{4-1.7}{x}} \\ \alpha (x)=\arctan {\displaystyle \frac{5}{x}}-\arctan {\displaystyle \frac{2.3}{x}} \\ {\alpha }^{\mathrm{\prime }}(x)=-{\displaystyle \frac{5}{x^2+25}}+{\displaystyle \frac{2.3}{x^2+5.29}} \\ {\alpha }^{\mathrm{\prime }}(x)=0 \\ {\displaystyle \frac{5}{x^2+25}}={\displaystyle \frac{2.3}{x^2+5.29}} \\ x=\sqrt{5\cdot 2.3}=3.39\text{ m} \end{gathered}$$

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