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 result:

A =  34.919 °

Solution:

a=16 m b=18 m c=27 m  a2=b2+c22 b c cosA  x=a2+b2+c22 b c=162+182+2722 18 277979720.82  A=180πarccos(x)=180πarccos(0.82)=34.919=345510"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)=34.919 ^\circ =34^\circ 55'10"

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