Find the area of a rectangle whose diagonal is 5, and the sine of the angle between them is 0.6.

The diagonal of the rectangle forms a right-angled triangle, the legs of which are the sides of the rectangle, and it itself is the hypotenuse.

Through the sine of the angle and the hypotenuse, we find the leg opposite to this angle.

a = 5 cm * 0.6 = 3 cm.

Let’s find the second leg according to the Pythagorean theorem.

b = √ (5 cm) ² – (3 cm) ² = √ (25 cm² – 9 cm²) = 4 cm.

Find the area of the rectangle.

S = 3 cm * 4 cm = 12 cm².

Answer: the area of the rectangle is 12 cm².