Big tower

From a tower 15 meters high and 30 meters away from the river, the width of the river appeared at an angle of 15°. How wide is the river in this place?

Correct answer:

w =  43.3 m

Step-by-step explanation:

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

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