One of the acute corners of a right-angled triangle is 2 times smaller than the other, and the difference between

One of the acute corners of a right-angled triangle is 2 times smaller than the other, and the difference between the hypotenuse and the smallest leg is 15 cm. Find a hyotenuse and a smaller leg.

From the condition, we know that one of the acute angles of a right-angled triangle is 2 times larger 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 smaller acute angle of the triangle, then 2x is the second acute angle.

x + 2x = 90;

3x = 90;

x = 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 triangle.

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