In the triangle, the sides a = 3, b = 2√3 are given. The angle A, which lies opposite the side a

In the triangle, the sides a = 3, b = 2√3 are given. The angle A, which lies opposite the side a, is equal to 60 degrees. Find a third party

We will use the well-known theorem of sines, in order to determine what the angle is opposite to the side in:

sin 60 ° / 3 = sin in / 2√3;

sin in = sin 60 ° / 3 * 2√3;

sin in = √3 / 2: 3 * 2√3 = 1.

This means that the angle B is equal to 90 °, that is, this triangle will be rectangular.

Let us then determine what the unknown side will equal, for which we use the well-known equation from the Pythagorean theorem:

√ ((2√3) ^ 2 – 3 ^ 2) = √12 – 9 = √3.

Answer: Under these initial conditions, the third party is equal to √3.