Final answer:
Trigonometry works because of the relationship between the angles and sides of right-angled triangles and the concept of similar triangles with equal side ratios.
Step-by-step explanation:
Trigonometry works because it is based on the relationship between the angles and sides of right-angled triangles.
The trigonometric ratios, such as sine, cosine, and tangent, are defined in terms of the adjacent side, opposite side, or hypotenuse of a triangle.
One of the main reasons why trigonometry works is because of the concept of similar triangles, where triangles with equal side ratios have equal angles.
This allows us to apply the same trigonometric ratios to different triangles and obtain accurate results.
So, option A: Trig uses similar triangles which have equal side ratios, is the correct statement explaining why trigonometry works.