Reflector

The circular reflector throws a light cone with a vertex angle 56° and is on 24 m height tower. The axis of the light beam has the axis of the tower angle 11°.

What is the maximum length of the illuminated horizontal plane?

Final Answer:

x =  26.77 m

Step-by-step explanation:

$$\begin{gathered} \alpha =56{}^{\circ } \\ \beta =11{}^{\circ } \\ h=24\text{m} \\ \Phi =\beta +\alpha /2=11+56/2=39{}^{\circ } \\ \Psi =\beta -\alpha /2=11-56/2=-17{}^{\circ } \\ t=\tan \Phi -\tan \Psi =\tan 39°-\tan (-17)°=0.809784-(-0.305731)=1.11551 \\ x=h\cdot t=24\cdot 1.1155=26.77\text{m} \end{gathered}$$

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