Find the length of the leg BC of a right-angled triangle ABC with a right angle C, if it is known that AC = 2 root of 3 cm, and angle B = 30 °.

Given:
ABC – right triangle
Angle C – straight
AC = 2√3 cm
Angle B = 30 °
To find:
The length of the BC leg.
Decision:
In a right-angled triangle, the leg, opposite an angle of 30 degrees, is half the hypotenuse.
By the Pythagorean theorem:
AB ^ 2 = AC ^ 2 + BC ^ 2
AC = AB / 2
Hence, AB = 2AC = 2 * 2√3 = 4√3
ВС = √AB ^ 2-AC ^ 2 = √16 * 3-4 * 3 = √12 * 3 = √36 = 6
Answer: The length of the BC leg is 6.