Right-triangle sides have ratios {trigonometry}.
In triangles, length of side c opposite angle C relates to other-two side lengths a b {law of cosines} {cosine law} {cosine rule}: c^2 = a^2 + b^2 - 2 * a * b * cos(C). If opposite angle is right angle, making right triangle, cos(C) = 0 and c^2 = a^2 + b^2, the Pythagorean theorem.
In triangles, ratio of angle A sine to opposite-side a length is equal for all three sides {law of sines} {sine law} {sine rule} {sine formula}: sin(A) / a = sin(B) / b = sin(C) / c.
In triangle, (a - b) / (a + b) = tan((A - B)^0.5) / tan((A + B)^0.5) {tangent law}, where angles are A and B and opposite sides are a and b.
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Date Modified: 2022.0225