In right-angled triangles ABC where angle C = 90 degrees, angle B = 60 degrees. Distance from vertex

In right-angled triangles ABC where angle C = 90 degrees, angle B = 60 degrees. Distance from vertex C to hypotenuse AB = 8cm. Then what = AC?

Triangle ABC is rectangular, since according to the condition, the angle is C = 90 degrees;

The sum of the angles of the triangle is 180 degrees, the angle C = 90, and the angle B = 60, from here we find the angle A:

180 – 90 – 60 = 30 degrees;

The leg, which lies opposite an angle of 30 degrees, is equal to half of the hypotenuse, it follows that the BC side is equal to half of the ABC side 8/2 = 4 cm.

To find the side of the AC, let’s use the Pythagorean theorem: “The square of the hypotenuse is equal to the sum of the squares of the legs”;

Then AC ^ 2 = AB ^ 2 – BC ^ 2 = 64 – 16 = 48;

AC = 4 roots of three.

Answer: 4 roots out of three.