In triangle ABC, angle C = 90 ° and angle A = 30 ° AC = 50√3. Find AB.

From the existing school curriculum in geometry, we know well that the cosine of an angle can be calculated using the ratio of the leg adjacent to this angle to the hypotenuse.

In this case, such a leg is AC.

Let us determine what the hypotenuse AB will equal, when from the condition of the task we know that the length of the AC side is 50√3:

cos 30 °, according to the table, will be equal to √3 / 2;

50√3: √3 / 2 = 50 * 2 = 100.

Answer: Under these initial conditions, the side AB of our triangle will be equal to 100.