The two angles of a triangle are 60 degrees and 45 degrees, and the side opposite the larger of these angles

The two angles of a triangle are 60 degrees and 45 degrees, and the side opposite the larger of these angles is 3 roots of 2 cm Find the length of the side of the triangle that is opposite the smaller of these angles.

By the sine theorem, the sides of a triangle are proportional to the sines of the opposite angles:

a / sin α = b / sin β.

For a given triangle, you can write the following ratio: a / sin 45 ° = 3√2 / sin 60 °.

From here we can determine the side lying opposite the smaller of the given angles:

a = 3√2 * sin 45 ° / sin 60 ° = 3√2 * (√2 / 2) / (√3 / 2) = 2√3 cm.