One of the corners of a right-angled triangle is 30 degrees, and the difference between the hypotenuse

One of the corners of a right-angled triangle is 30 degrees, and the difference between the hypotenuse and the smaller leg is 5 cm. Find the sides of the triangle.

Let x be the smaller leg of a right-angled triangle;

Then (x + 5) is the hypotenuse;

sin 30 ° = 0.5;

x / (x + 5) = 0.5;

2x = x + 5;

2x – x = 5;

x = 5 cm – smaller leg;

x + 5 = 5 + 5 = 10 cm – hypotenuse;

the larger leg, according to the Pythagorean theorem, is √ (10² – 5²) = √75.