John we can chat here.. Reply me when you are free :)

@ffahim Hi

Hi... So can we discuss about the problem?

Suppose that the steepest slope on a hill is 40%. If a road goes directly up the hill, then the steepest slope on the road will also be 40%. If, instead, the road goes around the hill at an angle, then it will have a shallower slope. For example, if the angle between the road and the uphill direction, projected onto the horizontal plane, is 60°, then the steepest slope along the road will be 20%, which is 40% times the cosine of 60°. Can you explain me these lines

@JohnRennie

I did a diagram to show this:

Pls let me see :)

The gradient is the distance you move vertically divided by the distance you move horizontally. So if you go straight up the slope (the red line) the gradient is y/x. OK so far?

Yep

Sorry mom called me. Pls continue

In the problem you describe the gradient is 0.4, so y/x = 0.4.

Yeah

So now suppose you walk up the slope along the blue line.

Hmm

You end up going up by the same amount, y, but you had to walk farther to get there.

Umm... Wait

Yehhh

Yes the X will be greater.

@ffahim and since the gradient is y/x that means along the blue line the gradient is smaller. Yes?

Yes

If you walk up the blue line then the horizontal distance you moved is the dashed line below the blue line, wich is at an angle $\theta$ to the "stright up" path.

The two dashed lines form a right angled triangle so if we call the new distance d then:

Oh... Now I get it

d cosθ = x

Thanks a lot

Thank you so much

Cool :-)

Brother. (may I call u), my English is not so good. I have been finding difficulties to communicate with you guys. What can I do

Why not ask on interpersonal.stackexchange.com ?

Thank you once again