Question

Знайти кути трикутника якщо їх градусні міри відносяться як 3 до 4 і 5

Answer 1

Ответ:

1) Т.к. сумма углов треугольника равна 180°, то:

180° : (3 + 4 + 5) = 15° - одна часть

2) <1 = 3 × 15° = 45°

<2 = 4 × 15° = 60°

<3 = 5 × 15° = 75°

Answer 2

Finding the Angles of a Triangle

To find the angles of a triangle when their degree measures are in the ratio of 3:4:5, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Let's assume that the three angles of the triangle are 3x, 4x, and 5x, where x is a constant. According to the given ratio, we have:

- Angle 1: 3x - Angle 2: 4x - Angle 3: 5x

The sum of these angles should be equal to 180 degrees:

3x + 4x + 5x = 180

Simplifying the equation, we get:

12x = 180

Dividing both sides of the equation by 12, we find:

x = 15

Now that we know the value of x, we can substitute it back into the expressions for the angles to find their actual degree measures:

- Angle 1: 3x = 3 * 15 = 45 degrees - Angle 2: 4x = 4 * 15 = 60 degrees - Angle 3: 5x = 5 * 15 = 75 degrees

Therefore, the angles of the triangle with degree measures in the ratio of 3:4:5 are 45 degrees, 60 degrees, and 75 degrees.

I hope this helps! Let me know if you have any further questions.