<p>You can take the lengths of the bases of the triangle to be as long as you like.</p>
<p>Have you heard of sampling in data processing? What basically happens is that at regular intervals of time [like 0.2 seconds say], information is retrieved from analog data, and stored as digital data. </p>
<p>In the same way, if we take the lengths of the bases to be, say 2 cm, we will retrieve only certain values of the function…at regular intervals.
However, as the lengths of the triangles grow smaller, and ‘approach’ a point, a more accurate representation of the function can be approached.
Moreover, this gives rise to the idea of calculus. The lengths of the bases only approach the dimensions of a point. Hence, the concept of a triangle and hence an angle still exists.
In fact, it is this sentiment of ‘limits’ that gave rise to calculus. :)</p>
<p>Say, for example, I want to graph f(x)= sinx, as per my definition of function.</p>
<p>Then my graph will extend from infinity to a height in which an isoceles triangle will make an angle of 1 radian/degree. This is because the range of sin x is -1 to 1. Hence, as the value of sin x approaches 0 at x=0, the value of the angle which the triangles make will also approach 0. Hence, the graph will approach infnity. Hope this helps. :)</p>