The side of the rhombus is 20 and the acute angle is 60 degrees. The height of the rhombus

The side of the rhombus is 20 and the acute angle is 60 degrees. The height of the rhombus, dropped from the top of the obtuse angle, divides the side into two segments. What are the lengths of these segments?

1) The height of the rhombus forms a right-angled triangle with an angle of 60 °. Another acute angle is 30 ° (180 ° – 90 ° – 60 °). In such right-angled triangles, the leg opposite to an angle of 30 ° is equal to half the hypotenuse:

20/2 = 10 cm – the first segment;

20 – 10 = 10 cm – second segment.

Answer: The height divides the side of the rhombus into two equal 10 cm segments.

2) Square area:

S = a * a;

S = 8 * 8;

S = 64 cm².

Rectangle area:

S = a * b;

S = 2 * 3;

S = 6 cm².

Subtract the area of the cut rectangle from the area of the square:

64 – 6 = 58 cm² – the area of the remaining part.