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

| September 26, 2021 | education

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

It is known that the diagonals of a rhombus intersect at an angle of 90 °.

Hence, we can consider the right-angled triangle ADO.

The diagonals of the rhombus are halved by the intersection point, which means that the side of the triangle is OD = 24/2 = 12, AO = 5. The side of the rhombus can be found by the Pythagorean theorem. In a rhombus, all sides are equal.

Side * side = 5 * 5 + 12 * 12 = 25 + 144 = 169. So side is 13.

The sine of angle ADO is equal to the ratio of AO to the side of the rhombus. The sine is 5/13.

Answer: the side is 13. The sine of the given angle is 5/13.



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