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Given:

A = 120

B = 30

C = 30

a = 3

To find:

b

c

Solution:

b = 2

c = 2

Explanation:

The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the following equation:

A + B + C = 180

Substituting the known values into the equation, we get:

120 + 30 + 30 = 180

180 = 180

Since the sum of the angles in a triangle is always 180 degrees, we know that the given triangle is a valid triangle.

We are also given that a = 3. This means that the side opposite angle A is 3 units long. We can use this information to find the values of b and c.

b:

The ratio between the opposite side and the adjacent side in angle B is equal to the ratio between the opposite side and the adjacent side in angle A. Therefore, we can write the following equation:

(b/3) = (2/3)

Solving for b, we get:

b = 2

c:

The ratio between the opposite side and the adjacent side in angle C is equal to the ratio between the opposite side and the adjacent side in angle A. Therefore, we can write the following equation:

(c/3) = (2/3)

Solving for c, we get:

c = 2

Therefore, the values of b and c are 2 and 2, respectively.

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