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 the Upper and Lower stations?

Correct answer:

y =  1750 m

Step-by-step explanation:

$$\begin{gathered} c=3.5\text{ km}\to \text{ m}=3.5\cdot 1000\text{ m}=3500\text{ m } \\ A=30\text{ ° } \\ \sin A=y\mathrm{/}c \\ {A}_1=A\mathrm{°}\to \text{ rad}=A\mathrm{°}\cdot {\displaystyle \frac{\pi }{180}}=30\mathrm{°}\cdot {\displaystyle \frac{3.1415926}{180}}=0.5236=\pi \mathrm{/}6 \\ y=c\cdot \sin (A_1)=3500\cdot \sin (0.5236)=1750\text{ m} \end{gathered}$$

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