Given: Right Triangle-ABC. Angle C = 60 degrees. Angle B = 30 degrees.

Given: Right Triangle-ABC. Angle C = 60 degrees. Angle B = 30 degrees. Lying leg, on the opposite corner = 60 gr = 3√3. Find: leg, hypotenuse, area.

Let <C = 60 °; <B = 30 °; <A = 90 °. AB = 3√3;

We apply the formula to the leg against an angle of 60 °, indicating the sides of the triangle: (AB) = c = 3√3; (AC) = in; BC = a:

(AB) ^ 2 + (AC) ^ 2 = BC ^ 2; c ^ 2 + b ^ 2 = a ^ 2, since <B = 30 °, then b = a / 2, we get the following equation:

(a / 2) ^ 2 + (3√3) ^ 2 = a ^ 2; (3/4) * a ^ 2 = 27; a ^ 2 = 27 * (4/3) = 36; a = √36 = 6; hence, the hypotenuse a = 6. leg b = a / 2 = 5/2 = 3.

Area C = in * s / 2 = (3 * 3√3) / 2 = (9√3) / 2 = 4.5√3.

Answer: hypotenuse 6, area 4.5√3.