In a right-angled triangle ABC, angle A = 40 degrees, angle B is 90 degrees, and in triangle MNK, angles M, N

In a right-angled triangle ABC, angle A = 40 degrees, angle B is 90 degrees, and in triangle MNK, angles M, N, K are related as 5: 9: 4, AB = 10 cm, NM = 15 cm. What is the ratio of BC to KM?

In the МНК triangle, let the angle M = 5 * X0, then the angle H = 9 * X0, the angle K = 4 * X0.

Then 5 * X + 9 * X + 4 * X = 1800.

18 * X = 180.

X = 10.

Then the angle H = 900, angle K = 400, angle M = 500.

In the triangle ABC BC = AB / tg40, in the triangle МНК KM = MН / Sin40.

Then BC / MH = (10 / tg40) / (15 / Sin40) = 10 * Sin40 / 15 * tg40 = 2 * Cos40 / 3.

Answer: The ratio BC / MH is 2 * Cos40 / 3.