The angle of view

Determine the angle of view at which the observer sees a rod 16 m long when it is 18 m from one end and 27 m from the other.

Correct answer:

A =  34.9193 °

Step-by-step explanation:

$$\begin{gathered} a=16\text{ m } \\ b=18\text{ m } \\ c=27\text{ m } \\ {a}^2=b^2+c^2-2\cdot b\cdot c\cdot \cos A \\ x={\displaystyle \frac{-a^2+b^2+c^2}{2\cdot b\cdot c}}={\displaystyle \frac{-16^2+18^2+27^2}{2\cdot 18\cdot 27}}={\displaystyle \frac{797}{972}}\doteq 0.82 \\ A={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arccos (x)={\displaystyle \frac{180\mathrm{°}}{\pi }}\cdot \arccos (0.82)=34.9193\text{°}=34\mathrm{°}55^{\mathrm{\prime }}10\mathrm{"} \end{gathered}$$

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