# River

From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.

Result

y =  29.5 m

#### Solution:

$h=11 \ \text{m} \ \\ x=24 \ \text{m} \ \\ A=13 ^\circ \rightarrow\ \text{rad}=13 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =13 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =0.22689 \ \\ B=\arctan (x/h)=\arctan (24/11) \doteq 1.141 \ \\ C=A+B=0.2269+1.141 \doteq 1.3679 \ \text{rad} \ \\ c=180/\pi \cdot \ C=180/3.1416 \cdot \ 1.3679 \doteq 78.3764 \ ^\circ \ \\ \tan C=(x+y)/h \ \\ y=h \cdot \ \tan(C)-x=11 \cdot \ \tan(1.3679)-24 \doteq 29.4762 \doteq 29.5 \ \text{m}$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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