Part 2/5:
Let’s consider a simple scenario involving two triangles where the angles are the same. Imagine a larger triangle and a smaller triangle nested within it. Both triangles share an angle, denoted as theta (θ), resulting in proportional relationships between their sides.
For example, if the bases of these triangles are equal, we can express the relationship between the sides using trigonometric functions. Specifically, the tangent of angle θ can be expressed as the ratio of the opposite side to the adjacent side of each triangle. For triangle one (the larger one), this might look like ( \tan(θ) = \frac{a}{2} ), while for triangle two (the smaller one), it could be ( \tan(θ) = \frac{3}{4} ).