In triangle Abc, angle C is 90, bc = 15, cosA = root 26/26. Find AC.

In triangle abc we find ac.
It is known:
Angle C is 90 °;
bc = 15;
cos A = √26 / 26.
Decision.
1) Find the sine of the angle a from the formula sin ^ 2 a + cos ^ 2 a = 1;
sin ^ 2 a = 1 – cos ^ 2 a;
sin a = √ (1 – cos ^ 2 a);
sin a = √ (1 – (√26 / 26) ^ 2) = √ (1 – 26 / (26 * 26)) = √ (1 – 1/26) = √25 / √26 = 5 / √26;
2) Find the tangent of angle A.
tg a = sin a / cos a;
tg a = 5 / √26 / (√26 / 26) = 5 / √26 * 26 / √26 = 5 * 26 / √26 ^ 2 = 5 * 26/26 = 5;
3) Find ac from the formula tg a = bc / ac;
Hence, ac = sun / tg a;
ac = 15/5 = 3;
As a result, we got that ac = 3.
Answer: ac = 3.