Question

Діагональ прямокутника дорівнює 6 см і утворює кут 25° з однією з його сторін. Знайдіть кут, що утворює діагональ з іншою стороною, та сторони прямокутника ( з точністю до сотих см) даю 100 балів

Answer 1

Given Information:

- Diagonal of a rectangle = 6 cm - Diagonal forms a 25° angle with one of its sides

Finding the Angle:

To find the angle formed by the diagonal with the other side of the rectangle, we can use the fact that opposite angles in a rectangle are congruent. Since the diagonal forms a 25° angle with one side, the opposite angle will also be 25°. Therefore, the angle formed by the diagonal with the other side of the rectangle is 25°.

Finding the Sides:

To find the lengths of the sides of the rectangle, we can use trigonometric ratios. Since we know the diagonal and one of the angles, we can use the sine and cosine functions.

Let's assume the length of the side forming the 25° angle is 'a' and the length of the other side is 'b'.

Using the sine function: sin(25°) = a / 6 a = 6 * sin(25°)

Using the cosine function: cos(25°) = b / 6 b = 6 * cos(25°)

Calculating the values using a calculator, we find: a ≈ 2.54 cm (rounded to the nearest hundredth) b ≈ 5.41 cm (rounded to the nearest hundredth)

Therefore, the length of the side forming the 25° angle is approximately 2.54 cm and the length of the other side is approximately 5.41 cm.

Note: The lengths are rounded to the nearest hundredth of a centimeter.

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