Question

Пряма ао перпендикулярна до площини кола з центром о. точка В лежить на колі. знайдіть відрізок Оа якщо радіус кола дорівнює 6 см, угол аво =45°

Answer 1

Получаем прямоугольный треугольник ABO, где угол ABO=45°,

тогда АО=ВО=6 см

Answer 2

Problem Analysis

We are given a circle with center O and radius 6 cm. Point B lies on the circle. We need to find the length of segment OA, given that angle AVO is 45°.

Solution

To find the length of segment OA, we can use trigonometry. Since angle AVO is 45° and AV is the radius of the circle, we can use the sine and cosine functions to find the lengths of the sides of the right triangle OAV.

Let's denote the length of segment OA as x.

Using the sine function: sin(AVO) = OA / AV sin(45°) = x / 6

Simplifying the equation: x = 6 * sin(45°)

Using a calculator, we can find the value of sin(45°) to be approximately 0.7071.

Substituting the value: x = 6 * 0.7071

Calculating the value: x ≈ 4.2426 cm

Therefore, the length of segment OA is approximately 4.2426 cm.

Conclusion

The length of segment OA is approximately 4.2426 cm, given that the radius of the circle is 6 cm and angle AVO is 45°.