Question

Дано: АВСД-прямоугольник,АС-диагональ, АС=3 см, угол САД= 37 градусов,Найти: S прямоульника - ?

Answer 1

АСD = а < 37 град. 
sin a = CD / AC => CD=AC * sin a = 3sin a 
cos a = AD/AC => AD =AC * cos a = 3cos a 

S = AB * AD = 3sin a * 3 cos a = 9 sin a* cos a = 9 * {sin (a+a) + sin(a-a)} / 2 = 
= 9/2 * sin 2a = 4 1/2 sin 2a

Answer 2

все правильно, только добавлю:
S=9/2 sin 2 α =9/2sin 74°≈9/2 *0.96≈4.32

Answer 3

Finding the Area of Rectangle ABCD

Given: - Rectangle ABCD - Diagonal AC = 3 cm - Angle CAD = 37 degrees

To find: - The area (S) of the rectangle

Solution

To find the area of the rectangle, we can use the formula: S = a * b, where a and b are the sides of the rectangle.

First, let's find the sides of the rectangle using the given information.

Finding the Sides of the Rectangle

We can use the given diagonal and the angle to find the sides of the rectangle.

Using trigonometric functions, we can find the sides of the rectangle: - a = AC * cos(CAD) - b = AC * sin(CAD)

Given: - AC = 3 cm - CAD = 37 degrees

Using the trigonometric functions, we can calculate the sides of the rectangle: - a = 3 * cos(37°) - b = 3 * sin(37°)

Calculating the Sides

- a ≈ 2.39 cm - b ≈ 1.83 cm

Finding the Area

Now that we have the sides of the rectangle, we can find the area using the formula S = a * b.

Substituting the values: - S ≈ 2.39 cm * 1.83 cm - S ≈ 4.37 cm²

So, the area of the rectangle ABCD is approximately 4.37 cm².