Steps

Find the height between the two floors if you know that the number of steps between the two floors is 18, the gradient is 30º and the length of the step is 28.6 cm. Report the result in centimeters to the nearest centimeter.

Result

x =  297 cm

Solution:

n=18 A=30 rad=30 π180 =30 3.1415926180 =0.5236=π/6 a=28.6 cm  tanA=x1a=16.512228.6=0  x1=a tan(A)=28.6 tan(0.5236)16.5122 cm  x=n x1=18 16.5122297.2199297 cmn=18 \ \\ A=30 ^\circ \rightarrow\ \text{rad}=30 ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =30 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =0.5236=π/6 \ \\ a=28.6 \ \text{cm} \ \\ \ \\ \tan A=\dfrac{ x_{1} }{ a }=\dfrac{ 16.5122 }{ 28.6 }=0 \ \\ \ \\ x_{1}=a \cdot \ \tan(A)=28.6 \cdot \ \tan(0.5236) \doteq 16.5122 \ \text{cm} \ \\ \ \\ x=n \cdot \ x_{1}=18 \cdot \ 16.5122 \doteq 297.2199 \doteq 297 \ \text{cm}



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