Finding lengths of a triangle with only one angle and its length.

Question

I have a paint program that does not deal with angles. Drawing a straight line will only get point of origin and length, no matter where you draw it to. So, I need to draw a line 570 mm or pixels, at a 35 degree angle. Thus I need the vertical length, and horizontal length to fix my points on.

Answer 1

A line of length $l$ starting at the origin of the plane and making an acute angle of $\theta$ with the positive $x$-axis will have coordinates $(l\cos\theta,l\sin\theta)$. Here $\sin\theta$ and $\cos\theta$ are the sine and cosine trigonometric functions.

Answer 2

Starting at point $(0,0)$ and proceeding in a northeast direction:

$$x_2 = 570\times\cos(35^\circ) = 466.9$$ $$y_2 = 570\times\sin(35^\circ) = 326.9$$