In rhombus ABCD, the length of the diagonal AC is 10 cm, and the diagonal BD is 24 cm

In rhombus ABCD, the length of the diagonal AC is 10 cm, and the diagonal BD is 24 cm, O is the point of intersection of the diagonals. Calculate: a) the length of the rhombus side; b) sine of the angle ADO.

Since it is known from the properties of the diagonals of the rhombus that they intersect at right angles. So from this property we can find out the diagonal by the Pythagorean theorem, knowing that the legs are half of the diagonals:
AB ^ 2 = (AO / 2) ^ 2 + (BO / 2) ^ 2.
AB ^ 2 = 5 ^ 2 + 12 ^ 2.
AB ^ 2 = 169 /
AB = 13.
The ADO angle will be 90 degrees (see the properties of the rhombus diagonals) sin 90 = 1
sin ADO = 1.
Answer: diagonal AB = 13, sin of angle ADO = 1.