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:

$h = 11 \ m \ \\ x = 24 \ m \ \\ A = (13^\circ \rightarrow rad) = (13 \cdot \ \dfrac{ \pi }{ 180 } \ ) = 0.226892802759 \ \\ B = \arctan (x/h) = \arctan (24/11) \doteq 1.141 \ \\ C = A+B = 0.2269+1.141 \doteq 1.3679 \ rad \ \\ c = 180/\pi \cdot \ C = 180/3.1416 \cdot \ 1.3679 \doteq 78.3764 \ ^\circ \ \\ \tan C = (x+y)/h \ \\ y = h \cdot \ \tan(C)-x = 11 \cdot \ \tan(1.3679)-24 \doteq 29.4762 = 29.5 \ \text { m }$

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