The cable car

The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?

Result

y =  1750 m

Solution:

c=3.5 km→m=3.5⋅ 1000 m=3500 m A=30 ∘  sin⁡A=y/c  A1=A∘→ rad=A∘⋅ π180 =30∘⋅ 3.1415926180 =0.5236=π/6  y=c⋅ sin⁡(A1)=3500⋅ sin⁡(0.5236)=1750 mc=3.5 \ km \rightarrow m=3.5 \cdot \ 1000 \ m=3500 \ m \ \\ A=30 \ ^\circ \ \\ \ \\ \sin A=y / c \ \\ \ \\ A_{1}=A ^\circ \rightarrow\ \text{rad}=A ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ =30 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ =0.5236=π/6 \ \\ \ \\ y=c \cdot \ \sin(A_{1})=3500 \cdot \ \sin(0.5236)=1750 \ \text{m}

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