Climb

On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road.

What is the height difference that car went?

Result

x =  433.4 m

Solution:

 p=8.7%=0.087  x=100050.0871+0.0872=433.4 m  α=arcsin(x5 km)=45820" \ \\ p = 8.7 \% = 0.087 \ \\ \ \\ x = 1000\cdot 5 \cdot \dfrac{ 0.087 }{ \sqrt{1 + 0.087^2}} = 433.4 \ \text{m} \ \\ \ \\ \alpha = \arcsin( \dfrac{x}{ 5 \ km } ) = 4^\circ 58'20"



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