One of the acute corners of a right-angled triangle is half the size of the other, and the difference

One of the acute corners of a right-angled triangle is half the size of the other, and the difference between the hypotenuse and the smaller leg is 15 cm. Find the hypotenuse and the smaller leg.

From the condition, we know that one of the acute angles of a right-angled triangle is 2 times smaller than the other, and the difference between the hypotenuse and the smaller leg is 15 cm.

Let’s find the sharp corners of the triangle. Let’s denote by x the larger acute angle of the triangle, then x / 2 is the second acute angle.

x + x / 2 = 90;

3x = 180;

x = 60 ° – larger angle, then smaller 60/2 = 30 °

It is known that a leg opposite to an angle of 30 ° is equal to half of the hypotenuse, and it is also known that opposite the smaller angle of a right-angled triangle lies the smaller side.

Let’s compose and solve the equation.

Let the smallest leg be equal to y and the hypotenuse equal to 2y.

Based on the condition:

2y – y = 15;

y = 15 cm smaller leg of a right-angled triangle.

We are looking for the hypotenuse: 2y = 2 * 15 = 30 cm.