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

August 22, 2021 | education

| **One of the corners of a right-angled triangle is 30 degrees, and the difference between the hypotenuse and the smaller leg is 4 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 30 °, and the difference between the hypotenuse and the smaller leg is 4 cm.

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 x and the hypotenuse be 2x.

Based on the condition:

2x – x = 4;

x = 4 cm smaller leg of a right-angled triangle.

We are looking for the hypotenuse: 2x = 2 * 4 = 8 cm.