In a right-angled triangle ABC, angle C is a straight line, AB = 26, legs are related as 5:12. Find a larger leg.

Let x be one conditional part of the legs. Then the smaller AC leg will be 5x parts, and the larger BC leg will have 12x parts. Let’s compose the equation according to the Pythagorean theorem and solve it:

AC ^ 2 + BC ^ 2 = AB ^ 2;

(5x) ^ 2 + (12x) ^ 2 = 26 ^ 2;

25x ^ 2 + 144x ^ 2 = 676;

(25 + 144) x ^ 2 = 676;

169x ^ 2 = 676;

x ^ 2 = 676: 169;

x ^ 2 = 4;

x = √4;

x = 2.

BC = 12x = 12 * 2 = 24.

Answer: BC = 24.