Magnification hi?

You should try doing the ray diagram if you don't see why the image height is negative.

This should hint you that there are two cases when the image height is inverted when dealing with converging lens, and it depends on the distance of the focal length.

 

There will be similar triangles using geometrical optics. You can use the thin lens equation to find the image distance and the object height and distance to find the angle. Then using trigonometry one can find the image height.

 

You can use trigonometry. The object distance and object height are two sides of a right angled triangle. The image distance and image height will be two sides of a similar triangle. You can compute the image height knowing these facts through simple trigonometry.

 

Well obviously if you have any two of the variables in the magnification equation, that's another way of finding one of the heights. In that case you don't need to draw the diagram.