In triangle ABC, angle C is 90 degrees, angle A is 30 degrees, CB = 3 cm. Determine AC.

Let’s find the hypotenuse: by the property of a right-angled triangle, it is equal to double the length of the leg, which lies opposite an angle of 30 °. Then:

3 * 2 = 6 (cm).

Let the unknown leg AC be x cm.Applying the Pythagorean theorem, compose an equation and solve it:

x² + 3² = 6²;

x² = 36 – 9;

x² = 25;

x = 5.

Answer: The AC side is 5 cm.