The diagonal of the rectangle is 10 cm and makes an angle of 30 degrees with the side. Find the smaller side.

We are given a rectangle and the length of its diagonal is known – 10 cm. It is also known that the diagonal forms an angle with the side of the rectangle equal to 30 °. To find the smaller side of a rectangle, we will consider a right-angled triangle formed by the sides of the rectangle and the diagonal.

Let’s apply the following property of a right-angled triangle to find the smaller side:

The leg, lying opposite an angle of 30 °, is equal to half the hypotenuse.

In our case, the smaller side is the leg opposite an angle of 30 °.

The hypotenuse is the diagonal and it is 10 cm.

Smaller sides of a rectangle:

10: 2 = 5 cm.