Find the length of the leg BC of a right-angled triangle ABC with a right angle C if you know that: AC = 2√3 cm.

As you know, opposite an angle of 30̊̊ in a right-angled triangle lies a leg equal to half of the hypotenuse. It follows that:

AB = 2AC.

On the other hand, by the Pythagorean theorem, the side BC is equal to:

BC = √ (AB² – AC²).

Substituting the previous found value for AB into this expression, we get the following:

BC = √ ((2AC) ² – AC²) = √ (4AC² – AC²) = √3AC² = AC√3.

Now, instead of AC, we substitute its value and find the length of the leg BC:

BC = 2√3 * √3 = 2 * 3 = 6 cm.

Answer: the leg BC of the right-angled triangle ABC is 6 centimeters.