In triangle ABC, angle C is 90 degrees, BC = 1, cos B = 1 / √2, find AC.

Since C = 90 °, triangle ABC is right-angled with hypotenuse AB, then by determining the cosine of the angle, we get:

AB = BC / cos (B) = 1: 1 / √2 = √2.

Using the Pythagorean theorem, we get:

AC = √ (AB ^ 2 – BC ^ 2) = √ (2 – 1) = 1.

Answer: the required side length AC is equal to 1.




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