Question

В прямоугольнике диагональ равна 10 ,а угол между ней и одной из сторон равен 30 .найдите площадь срочно

Answer 1

Одна сторона получившегося треугольника  равна половине диагонали
 a=10/2=5 . Она лежит против угла 30 градусов
  другую сторону найдем по т. Пифагора 
   в²=с²-а²   в²=10²-5²=100-25=75   в=√75=√25*3=5√3
   S=a*b   S=5*5√3=25√3



 

Answer 2

Calculation of the Area of a Rectangle

To find the area of a rectangle, we need to know the length of its sides. In this case, we are given that the diagonal of the rectangle is 10 units and the angle between the diagonal and one of the sides is 30 degrees.

Let's denote the length of one side of the rectangle as a and the length of the other side as b. The diagonal of the rectangle can be represented as the hypotenuse of a right triangle, with the sides of the rectangle as its legs.

Using trigonometry, we can relate the angle and the sides of the right triangle as follows:

sin(30 degrees) = a / 10

Simplifying this equation, we can solve for a:

a = 10 * sin(30 degrees)

Similarly, we can relate the angle and the sides of the right triangle as follows:

cos(30 degrees) = b / 10

Simplifying this equation, we can solve for b:

b = 10 * cos(30 degrees)

Now that we have the lengths of the sides of the rectangle, we can calculate its area using the formula:

Area = a * b

Let's calculate the area using the given information.

Calculation:

Using the trigonometric identities, we can calculate the values of a and b:

a = 10 * sin(30 degrees) = 10 * 0.5 = 5 units

b = 10 * cos(30 degrees) = 10 * 0.866 = 8.66 units

Now, we can calculate the area of the rectangle:

Area = a * b = 5 * 8.66 = 43.3 square units

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

Please let me know if there is anything else I can help you with!