A 3-4-5 triangle and a 6-8-10 triangle
Legs 6 and 8 are exactly legs 3 and 4, doubled. Solving each: legs 3,4 gives hypotenuse 5, area 6, angles 36.8699° and 53.1301°. Legs 6,8 gives hypotenuse 10, area 24, angles 36.8699° and 53.1301° — the exact same two angles, even though the hypotenuse doubled and the area quadrupled.
Size scales linearly, angles don't scale at all
Doubling every side length doubles the hypotenuse and perimeter (both single lengths), but quadruples the area — 6 to 24 is exactly ×4 — because area is a product of two lengths, so doubling both multiplies the area by 2×2. Angles, though, come from a ratio (leg a ÷ leg b), and that ratio is unchanged by scaling both legs by the same factor: 3÷4 and 6÷8 are both exactly 0.75.
Confirming it with the general triangle solver
Feeding the full 3-4-5 side lengths into the general (all-three-sides) triangle solver, rather than the right-triangle-specific one, gives area 6, perimeter 12, and angles 36.8699°, 53.1301°, and exactly 90° for the third angle — matching the right-triangle calculator's result precisely, and confirming that a 90° angle emerges naturally from the 3-4-5 side lengths rather than being assumed in advance.
The everyday version of this idea
This is why a photograph enlarged to twice its size still looks like the same picture, and why a small scale drawing of a building can accurately represent its full-size angles. Two triangles with the same angles but different sizes are called "similar triangles" — the angles define the shape, and the side lengths define the size, and the two are independent.