In a rectangle, the diagonal is 32, and the angle between it and one of the sides is 60 °.

In a rectangle, the diagonal is 32, and the angle between it and one of the sides is 60 °. find the area of the rectangle divided by √3.

1. In a right-angled triangle formed by drawing a diagonal, the other acute angle is equal to:

180 ° – 90 ° – 60 ° = 30 °.

2. The diagonal in this triangle is the hypotenuse.

3. The leg, located opposite an angle of 30 °, is equal to 1/2 of the hypotenuse, that is, 32: 2 = 16 cm.

4. The other leg, according to the Pythagorean theorem, is equal to √32 – 16 = √1024 – 256 = √768 = √256 x 3 = 16√3 cm.

5. The area of the rectangle divided by √3 is 16 x 16√3 / √3 = 256 cm ^ 2.

Answer: the area of the rectangle divided by √3 is 256 cm ^ 2.