The area of a right-angled triangle is 882√3. one of the acute angles is 30 °. find the hypotenuse.

Let the length of the leg, against the angle of 300, be equal to X cm. BC = X cm.
Then the length of the hypotenuse AB = 2 * BC = 2 * X cm.
By the Pythagorean theorem, AC ^ 2 = AB ^ 2 – BC ^ 2 = 4 * X ^ 2 – X ^ 2 = 3 * X ^ 2.
AC = X * √3 cm.
Then the area of the triangle ABC is equal to:
Savs = 882 * √3 = X * X * √3 / 2.
X ^ 2 = 2 * 882 = 1764.
X = BC = 42 cm.
Then the hypotenuse AB = 2 * 42 = 84 cm.
Answer: The length of the hypotenuse is 84 cm.