Lodge view angle

The observer lies on the ground at a distance of 20 m from a hunting lodge 5 m high.
A) At what angle of view does the posed see?
B) How much does the angle of view change if it approaches the sitting by 5 m?

Final Answer:

α =  14.0362 °
γ =  4.3987 °

Step-by-step explanation:

$$\begin{gathered} x=20\text{m} \\ y=5\text{m} \\ \tan \alpha =y:x \\ \alpha =\frac{180°}{\pi }\cdot \arctan (y/x)=\frac{180°}{\pi }\cdot \arctan (5/20)=14.0362^{\circ }=14°2^{\prime }10" \end{gathered}$$

$$\begin{gathered} x_2=x-5=20-5=15\text{m} \\ \tan \beta =y:x_2 \\ \beta =\frac{180°}{\pi }\cdot \arctan (y/x_2)=\frac{180°}{\pi }\cdot \arctan (5/15)\doteq 18.4349{}^{\circ } \\ \gamma =\beta -\alpha =18.4349-14.0362=4.3987^{\circ }=4°23^{\prime }55" \end{gathered}$$

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