View angle - river

The 15 m high building is 30 m away from the river bank. The river's width can be seen from the roof of this building at an angle of 15°. How wide is the river?

Correct answer:

y =  43.3 m

Step-by-step explanation:

$$\begin{gathered} h=15\text{m} \\ x=30\text{m} \\ \alpha =15°\to \text{rad}=15°\cdot \frac{\pi }{180}=15°\cdot \frac{3.1415926}{180}=0.2618=\pi /12\text{rad} \\ \beta =\arctan (x/h)=\arctan (30/15)\doteq 1.1071\text{rad} \\ \gamma =\alpha +\beta =0.2618+1.1071\doteq 1.3689\text{rad} \\ {\gamma }_2=180/\pi \cdot \gamma =180/3.1416\cdot 1.3689\doteq 78.4349{}^{\circ } \\ \tan \gamma =(x+y)/h \\ y=h\cdot \tan \gamma -x=15\cdot \tan 1.3689-30=25\sqrt{3}=43.3\text{m} \end{gathered}$$

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