Question

диагональ прямоугольника равна 10 а угол между диагоналями равен 60,НАЙДИТЕ ПЛОЩАДЬ.

Answer 1

Площадь прямоугольника можно найти как  1/2 произведения его  диагоналей на синус угла между ними. 

S=(AC x BD):2 x Sin60, S=(10 x 10):2 x  √3/2= 25 √3 

Answer 2

Finding the Area of a Rectangle with Given Diagonal and Angle Between Diagonals

To find the area of a rectangle when the diagonal is given as 10 and the angle between the diagonals is 60 degrees, we can use the following steps:

1. Calculate the Length and Width of the Rectangle: - The diagonal of a rectangle can be used to find the length and width of the rectangle using trigonometric functions.

2. Use the Length and Width to Calculate the Area: - Once the length and width are determined, the area of the rectangle can be calculated using the formula: Area = Length * Width.

Calculation Steps

1. Calculate the Length and Width of the Rectangle: - The diagonal of the rectangle, denoted as D, is given as 10. - The angle between the diagonals, denoted as θ, is given as 60 degrees.

Using the formula for the length and width of a rectangle in terms of the diagonal and the angle between the diagonals: - Length, L = D * cos(θ) - Width, W = D * sin(θ)

Applying the given values: - Length, L = 10 * cos(60°) = 10 * 0.5 = 5 - Width, W = 10 * sin(60°) = 10 * √3/2 ≈ 8.66

2. Use the Length and Width to Calculate the Area: - Area = Length * Width - Area ≈ 5 * 8.66 ≈ 43.3 square units

Therefore, the area of the rectangle is approximately 43.3 square units.

(#1)