In a right angle triangle with a constant angle, what happens to the ratio of the sides and hypotenuse?

In a right angle triangle where one angle is held constant, the sides' ratios remain constant regardless of the triangle's size. This is because the ratios of the sides to the hypotenuse are determined by the angles of the triangle, which are fixed in this case.

For any right triangle, the trigonometric ratios (sine, cosine, and tangent) that relate the angles to the lengths of the sides are defined and will not change as the dimensions of the triangle are scaled up or down. For instance, if one angle is fixed at 30 degrees, the lengths of the opposite and adjacent sides will always maintain the same ratio to the hypotenuse, ensuring that various measurements of that triangle will yield the same proportions.

This principle applies to all similar triangles, where corresponding angles are equal and corresponding sides are in proportion, thus reaffirming that the ratio of the sides to the hypotenuse will remain constant with a constant angle in a right triangle.