Question

40 БАЛЛОВ , СРОЧНО ! * * * Прямокутний трикутник з кутом 20 градусів і гіпотенузою 14 см вписано в круг. Знайти площу найменшого з сегментів , який відтинається сторонами трикутника . Відповідь округлити до десятих.

Answer 1

Відповідь:

Пояснення:

розв'язання завдання додаю

Срочно - терміново

Answer 2

To find the area of the smallest segment cut off by the sides of the triangle, we first need to find the radius of the circle.

We can use the fact that the hypotenuse of the triangle is the diameter of the circle. The hypotenuse is given as 14 cm, so the radius of the circle is half of that, which is 7 cm.

Next, we need to find the length of the two legs of the triangle. Since the triangle is a right triangle, we can use trigonometric ratios to find the lengths of the legs.

Let's call the length of one leg x. Using the sine function, we can write the equation:

sin(20°) = x / 14

Solving for x, we find:

x = 14 * sin(20°) ≈ 4.77 cm

Now, we can find the length of the other leg by using the Pythagorean theorem:

leg^2 + leg^2 = hypotenuse^2

x^2 + leg^2 = 14^2

leg^2 = 14^2 - x^2

leg ≈ sqrt(14^2 - 4.77^2) ≈ 12.91 cm

Now that we have the lengths of the legs, we can find the area of the triangle using the formula:

Area = (base * height) / 2

The base of the triangle is one of the legs, which is approximately 4.77 cm, and the height is the other leg, which is approximately 12.91 cm.

Area = (4.77 * 12.91) / 2 ≈ 30.84 cm^2

Therefore, the area of the smallest segment cut off by the sides of the triangle is approximately 30.84 cm^2.