The legs of a right-angled triangle are equal to 26√ and 1. Find the sine of the smallest angle of this triangle.

To solve this problem, remember that the sine of the angle is equal to the ratio of the opposite leg to the hypotenuse. We can calculate the hypotenuse by the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs.
Knowing that one leg is 26 cm, and the other is 1, we calculate the hypotenuse.
c ^ 2 = 26 * 26 + 1 * 1 = 676 + 1 = 677
c = √677 centimeters.
Recall that a triangle has a smaller angle opposite the smaller side. Assuming that the smaller side is 1 cm, we calculate the sine.
sin (A) = 1 / √677.
Answer: 1 / √677.