# One of the corners of the rectangular triangle is equal to 30 °, and the difference in hypotenuses

**One of the corners of the rectangular triangle is equal to 30 °, and the difference in hypotenuses and a smaller category-5 cm. Find these sides of the triangle.**

1. The condition of the task is set by a rectangular triangle.

It is known that one of its corners is equal to 30 °.

In a rectangular triangle, the side of him opposite is equal to half of the hypotenuse.

Denote the length of the category for x, then the length of the hypotenuse – 2 * H.

2. The corners in the triangle are equal to 30 °, 60 ° and 90 °.

Little side lies against a smaller corner.

The task says that the difference in hypotenuse and a smaller category is 5 cm.

Then 2 * x – x = 5.

x = 5 cm – smaller catat.

2 * x = 2 * 5 = 10 cm = hypotenuse.

3. Calculate the square of the third party on the Pythagora theorem.

10 * 10 – 5 * 5 = 100 – 25 = 75 = 25 * 3.

Then the second catat is equal to 5√3.

Answer: The sides of the triangle 5, 5√3 and 10.