Ditch

Ditch profile is an isosceles trapezoid with bases of length 80m and 60m. The slope of the side wall of the ditch is 80°. Calculate the ditch depth.

Result

h =  56.713 m

Solution:

a=80 m c=60 m x=(a−c)/2=(80−60)/2=10 m tan⁡80∘=h/x  h=x⋅ tan⁡(80∘→rad)=x⋅ tan⁡(80∘⋅ π180 )=10⋅ tan⁡(80∘⋅ 3.1415926180 )=56.71282=56.713  m a = 80 \ m \ \\ c = 60 \ m \ \\ x = (a-c)/2 = (80-60)/2 = 10 \ m \ \\ \tan 80^\circ = h/x \ \\ \ \\ h = x \cdot \ \tan( 80 ^\circ \rightarrow rad) = x \cdot \ \tan( 80 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ ) = 10 \cdot \ \tan( 80 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ ) = 56.71282 = 56.713 \ \text{ m }

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