Question

solve 18 question in full solution

Answer 1

The diagonals of a rhombus cross at

90°

The length from the center to one diagonal is equal to the length from the center to the opposite diagonal.

In this case a right angled triangle is formed and thus we can use the Pythagoras theorem to get the hypotenuse which is the length.

We will find this in the diagram.

From the rhombus ABCD with center O, we form a right angled triangle DOC.

It's lengths are 4 cm and 3 cm for the longer side and shorter side respectively.

We need to work out the hypotenuse in order to use the trigonometric ratios to get sin of OCD.

From pythogras theorem :

Hypotenuse = √(3² + 4²) = √25 = 5cm

Sin = opposite / hypotenuse

Sin = OD / 5

OD = 3cm

Sin = 3 / 5 = 0.6