Question

Знайдіть гострі кути прямокутного трикутника якщо кут між висотою і бісектрисою проведеними з вершини прямокутного кута дорівнює 20° ​

Answer 1

Ответ:

вот решение

Объяснение:

на листочке

Answer 2

Finding the acute angles of a right triangle

To find the acute angles of a right triangle, we need to use the information given in the question. The question states that the angle between the height and the bisector drawn from the vertex of the right angle is 20°.

Let's assume that the right angle is at vertex A, and the height is drawn from vertex A to the hypotenuse BC. The bisector is drawn from vertex A to the midpoint of the hypotenuse BC.

To find the acute angles, we can use the following steps:

1. Let's label the acute angles as ∠B and ∠C, with ∠B being the angle opposite to side AB and ∠C being the angle opposite to side AC.

2. Since the bisector divides the right angle into two equal angles, we have ∠BAC = ∠CAB = 20°.

3. We know that the sum of the angles in a triangle is 180°. In a right triangle, one angle is always 90°. Therefore, we can write the equation: ∠B + ∠C + 90° = 180°.

4. Rearranging the equation, we get: ∠B + ∠C = 90°.

5. Substituting the value of ∠BAC (which is 20°) into the equation, we get: 20° + ∠C = 90°.

6. Solving for ∠C, we find: ∠C = 90° - 20° = 70°.

7. Finally, substituting the value of ∠C into the equation, we find: ∠B + 70° = 90°.

8. Solving for ∠B, we find: ∠B = 90° - 70° = 20°.

Therefore, the acute angles of the right triangle are ∠B = 20° and ∠C = 70°.

Please note that the assumption made in this explanation is based on the given information. If there are any additional details or specific conditions mentioned in the question, please provide them for a more accurate answer.