In triangle ABC BC = 5√3, angle A = 60, angle B = 45. Find the side of the speaker.

According to the theorem of sines, the ratios of the sides to the sines of the angles opposite to them are equal to each other. Also, these ratios are equal to the diameter of the circle circumscribed about this triangle.

It turns out that the relationship will look like this:

BC / sin ⦟A = AC / sin ⦟B.

Substitute the known values and get the proportion:

5 * √ (3) / (√ (3) / 2) = BC / (√ (2) / 2).

From here we find BC:

5 * 2 = 2 * BC / √ (2);

BC = 5 * √ (2).

Answer: BC = 5 * √ (2).