Question

Довести,що сума гострих кутів прямокутного трикутника дорівнює 90 градусів

Answer 1

Якщотрикутник прямокутний то внього один з кутів має 90* ,а оскільки сума кутів трикутника дорівнює 180*  то інші два кута дорівнюють 180*-90*=90*

Answer 2

The Sum of Angles in a Right Triangle

To prove that the sum of the angles in a right triangle is equal to 90 degrees, we can rely on the properties of triangles and the definition of a right triangle.

A right triangle is a triangle that has one angle measuring 90 degrees. This angle is called the right angle. The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees.

Let's consider a right triangle with sides a, b, and c, where c is the hypotenuse (the side opposite the right angle). The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem can be expressed as:

c^2 = a^2 + b^2 Now, let's examine the angles in a right triangle. We know that the sum of the angles in any triangle is always 180 degrees. Therefore, the sum of the two acute angles in a right triangle must be equal to 90 degrees (180 degrees - 90 degrees).

This can be proven by considering the following:

- Let's assume that angle A is one of the acute angles in the right triangle. - The other acute angle, angle B, can be determined by subtracting angle A from 90 degrees (the right angle). - The sum of angles A and B is equal to angle A + angle B = 90 degrees.

Therefore, the sum of the angles in a right triangle is indeed equal to 90 degrees.

In conclusion, the sum of the angles in a right triangle is always 90 degrees. This is a fundamental property of right triangles and can be proven using the Pythagorean theorem and the definition of a right triangle.