In triangle ABC, angle C is straight, AB = 2; in triangle ABC, angle C is straight, AB = 2 cm, angle B = 30 degrees

In triangle ABC, angle C is straight, AB = 2; in triangle ABC, angle C is straight, AB = 2 cm, angle B = 30 degrees, MC is perpendicular (ABC), MC = 0.5 cm. Find from point M to line AB

In a right-angled triangle ABC, the AC leg is located opposite an angle of 300, then the length of the AC leg = AB / 2 = 2/2 = 1 cm.

Let’s build the height CH of the right-angled triangle ABC.

In a right-angled triangle ACН, the angle СAН = (90 – 30) = 600.

Then Sin60 = CH / AC.

CH = AC * Sin60 = 1 * √3 / 2 cm.

In the right-angled triangle MCH, the segment MН is the desired distance, which, according to the Pythagorean theorem. MH ^ 2 = CM ^ 2 + CH ^ 2 = (1/4) + 3/4 = 4/4.

MH = 1 cm.

Answer: From point M to straight AB 1 cm.