The characteristics of similar triangles, originally formulated by Euclid, are the building blocks of trigonometry. Euclid's theorems state if two angles of one triangle have the same measure as two angles of another triangle, then the two triangles are similar. Also, in similar triangles, angle measure and ratios of corresponding sides are preserved. Because all right triangles contain a 90° angle, all right triangles that contain another angle of equal measure must be similar. Therefore, the ratio of the corresponding sides of these triangles must be equal in value. These relationships lead to the trigonometric ratios. Lowercase Greek letters are usually used to name angle measures. It doesn't matter which letter is used, but two that are used quite often are alpha (α) and theta (θ).
The function that best represents the data is y = 0.75x + 4.5. The slope in this case represents the increase in the amount she spends in $ due to the number of cards she makes. The intercept with the Y axis (4.5) means that she has an expense of 4.5 $ without having made any card yet.
