Math Is Fun Forum

lee butterworth

Member

Registered: 2006-02-25

Posts: 1

gradient & degree

hi i am a roofer. i am trying to find the formula for working out the gradient of a slope in relation to its degree. ie, what is the gradient of a 10 degree slope. thank you if you can help.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,240

Re: gradient & degree

The gradient of a line is the tangent of the angle of slope; that
is, the tangent of the angle between the line and the positive x axis.

The x axis has angle 0 with itself, so its gradient is tan(0) = 0.

The y axis makes an angle of 90 degrees with the x axis, and tan(90) = infinity,  So the y axis has infinite gradient.

Your question is what is the gradient of a 10 degree slope.
If the line makes an angle of 10 degrees with the positive X axis, the gradient is tan(10 degrees) or 0.17632698 approximately.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.