# 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.

Result

A =  34.919 °

#### Solution:

$a=16 \ \text{m} \ \\ b=18 \ \text{m} \ \\ c=27 \ \text{m} \ \\ \ \\ a^2=b^2+c^2 - 2 \cdot \ b \cdot \ c \cdot \ \cos A \ \\ \ \\ x=\dfrac{ -a^2+b^2+c^2 }{ 2 \cdot \ b \cdot \ c }=\dfrac{ -16^2+18^2+27^2 }{ 2 \cdot \ 18 \cdot \ 27 } \doteq \dfrac{ 797 }{ 972 } \doteq 0.82 \ \\ \ \\ A=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(x)=\dfrac{ 180^\circ }{ \pi } \cdot \arccos(0.82) \doteq 34.9193 \doteq 34.919 ^\circ \doteq 34^\circ 55'10"$

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