Get the slope from one point and an angle in degrees

In javascript, I am trying to draw a line that is at an angle that is user defined.

Basically, I have a point (x,y) and an angle to create the next point at. The length of the line need to be 10px.

Let's say that the point to start with is (180, 200)... if I give it angle "A" and the (I guess)hypotenuse is 10, what would my equation(s) be to get the X and Y for a slope?

Thanks for your help!

Solution

Assuming H = Hypotenuse (10 in your example), this is the formula for your slope:

Y2 = H(Sin(A)) + Y1
   = 10(Sin(A)) + 200

X2 = Sqrt((H^2)-(Y2^2)) + X1
   = Sqrt(100 - (Y2^2)) + 180

So now you've got

(180, 200) -> (X2, Y2)

Where X2, Y2 will vary depending on the values of A and H

To check our calculation - A (as entered by the user) can be calculated using the slope equation replacing the X1, X2, Y1 and Y2 values with the original input and resulting output.

A = InvTan((Y2 - Y1) / (X2 - X1))
  = InvTan((Y2 - 200) / (X2 - 180))