In triangle ABC, measure of angle A is equal to 30 degrees, AC is equal to 4 and AB is equal to 3 square root of 3. Find BC

use the law of cosines.

To find the length of BC in triangle ABC, we can use the Law of Cosines. The Law of Cosines states that in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab*cos(C)

In our case, we can label angle B as 90 degrees, since triangle ABC is a right triangle. So we have:

BC^2 = AB^2 + AC^2 - 2(AB)(AC)*cos(B)

Substituting the given values:

BC^2 = (3√3)^2 + 4^2 - 2*(3√3)*(4)*cos(90)

Simplifying the equation:

BC^2 = 27 + 16 - 24√3

BC^2 = 43 - 24√3

Now, to find the value of BC, we need to take the square root of both sides:

BC = √(43 - 24√3)

Please note that using a calculator or any other computational tool is essential at this point to get the exact value for BC.