A rhombus of side 10cm has obtuse angles of 110 degree sketch the rhombus, showing its diagonal and as many angles as possible. Hence calculate the length of the diagonals of the rhombus
First, let's sketch the rhombus:
```
/\
/ \
/ \
/ \
/ \
/__________\
10cm
```
The obtuse angle of 110 degrees will be at the top and bottom vertices of the rhombus. We can also draw the diagonals:
```
/\
/ \
/ \
/ | \
/ | \
/______|_____\
10cm
```
To calculate the length of the diagonals, we can use the Law of Cosines:
Let the length of one diagonal be $d$.
In the triangle formed by the diagonal, one side of the rhombus, and half of one of the acute angles (55 degrees), we have:
$d^2 = (10)^2 + (10)^2 - 2(10)(10)cos(55)$
$d^2 = 100 + 100 - 200cos(55)$
$d^2 = 200 - 200cos(55)$
$d^2 = 200 - 200 * 0.5736 (cosine of 55 degrees) = 200 - 114.72$
$d^2 = 85.28$
$d = \sqrt{85.28} \approx 9.24cm$
Therefore, the length of each diagonal of the rhombus is approximately 9.24cm.