Through the vertex of angle B, equal to 30 degrees of a right-angled triangle ABC

Through the vertex of angle B, equal to 30 degrees of a right-angled triangle ABC with a hypotenuse AB = 4 cm, a perpendicular BM = 3 cm is drawn. Calculate the distance from point M to line AC.

Since the ABC triangle is rectangular, and the AC leg lies opposite the angle 30, AC = AB / 2 = 4/2 = 2 cm.

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AB ^ 2 – AC ^ 2 = 16 – 4 = 12.

BC = 2 * √3 cm.

The distance from point M to line AC is the hypotenuse of the right-angled triangle BCM, then, according to the Pythagorean theorem, CM ^ 2 = BC ^ 2 + BM ^ 2 = 12 + 9 = 21.

CM = √21 cm.

Answer: From point M to line AC √21 cm.