The area of a right-angled triangle is 12.5 √ 3. One of the acute angles is 60 degrees. Find the length of the hypotenuse

The area of the triangle is equal to half the product of the tangent of the angle and the square of the adjacent leg;

S = 1/2 * b ^ 2 tq 60;

Since we know the value of the area S = 12.5 √3 and the tangent of the angle √3, we can determine the adjacent leg;

b ^ 2 = 12.5√3 * 2 / √3 = 25; b = 5;

This leg lies opposite the angle 30, which means it is equal to half of the hypotenuse, therefore, the hypotenuse is equal to a = 2 b = 10.